Note: Front Cover -- Praise -- Title Page -- Rights Page -- Contents -- Preface -- Chapter 1: Where is the Vision? -- Chapter 2: Other Worlds are Possible -- Chapter 3: Way Beyond Recycling - Off-the-Scale Alternatives to Stuff -- Chapter 4: After Transportation - Whole-System Redesign in the City -- Ahapter 5: Adaptation with Sass - Embracing Climate Change -- Chapter 6: A More-Than-Human World - Redesign for Connection -- Chapter 7: Fellowship with Animals - The Great Second Chance -- Chapter 8: The World's Great Liturgies - Toward a Celebratory Environmentalism -- Chapter 9: To the Stars - From Earthlings to Spacelings -- Chapter Notes -- Return of Thanks -- Index -- About the Author -- Books to Build a New Society.

Note: Front Cover -- Many-Sorted Algebras for Deep Learning and Quantum Technology -- Copyright Page -- Dedication -- Contents -- List of figures -- Preface -- Acknowledgments -- 1 Introduction to quantum many-sorted algebras -- 1.1 Introduction to quantum many-sorted algebras -- 1.1.1 Algebraic structures -- 1.1.2 Many-sorted algebra methodology -- 1.1.3 Global field structure -- 1.1.4 Global algebraic structures in quantum and in machine learning -- 1.1.5 Specific machine learning field structure -- 1.1.6 Specific quantum field structure -- 1.1.7 Vector space as many-sorted algebra -- 1.1.8 Fundamental illustration of MSA in quantum -- 1.1.9 Time-limited signals as an inner product space -- 1.1.10 Kernel methods in real Hilbert spaces -- 1.1.11 R-Modules -- References -- 2 Basics of deep learning -- 2.1 Machine learning and data mining -- 2.2 Deep learning -- 2.3 Deep learning and relationship to quantum -- 2.4 Affine transformations for nodes within neural net -- 2.5 Global structure of neural net -- 2.6 Activation functions and cost functions for neural net -- 2.7 Classification with a single-node neural net -- 2.8 Backpropagation for neural net learning -- 2.9 Many-sorted algebra description of affine space -- 2.10 Overview of convolutional neural networks -- 2.11 Brief introduction to recurrent neural networks -- References -- 3 Basic algebras underlying quantum and NN mechanisms -- 3.1 From a vector space to an algebra -- 3.2 An algebra of time-limited signals -- 3.3 The commutant in an algebra -- 3.4 Algebra homomorphism -- 3.5 Hilbert space of wraparound digital signals -- 3.6 Many-sorted algebra description of a Banach space -- 3.7 Banach algebra as a many-sorted algebra -- 3.8 Many-sorted algebra for Banach* and C* algebra -- 3.9 Banach* algebra of wraparound digital signals -- 3.10 Complex-valued wraparound digital signals -- References. , 4 Quantum Hilbert spaces and their creation -- 4.1 Explicit Hilbert spaces underlying quantum technology -- 4.2 Complexification -- 4.3 Dual space used in quantum -- 4.4 Double dual Hilbert space -- 4.5 Outer product -- 4.6 Multilinear forms, wedge, and interior products -- 4.7 Many-sorted algebra for tensor vector spaces -- 4.8 The determinant -- 4.9 Tensor algebra -- 4.10 Many-sorted algebra for tensor product of Hilbert spaces -- 4.11 Hilbert space of rays -- 4.12 Projective space -- References -- 5 Quantum and machine learning applications involving matrices -- 5.1 Matrix operations -- 5.2 Qubits and their matrix representations -- 5.3 Complex representation for the Bloch sphere -- 5.4 Interior, exterior, and Lie derivatives -- 5.5 Spectra for matrices and Frobenius covariant matrices -- 5.6 Principal component analysis -- 5.7 Kernel principal component analysis -- 5.8 Singular value decomposition -- References -- 6 Quantum annealing and adiabatic quantum computing -- 6.1 Schrödinger's characterization of quantum -- 6.2 Quantum basics of annealing and adiabatic quantum computing -- 6.3 Delta function potential well and tunneling -- 6.4 Quantum memory and the no-cloning theorem -- 6.5 Basic structure of atoms and ions -- 6.6 Overview of qubit fabrication -- 6.7 Trapped ions -- 6.8 Super-conductance and the Josephson junction -- 6.9 Quantum dots -- 6.10 D-wave adiabatic quantum computers and computing -- 6.11 Adiabatic theorem -- Reference -- Further reading -- 7 Operators on Hilbert space -- 7.1 Linear operators, a MSA view -- 7.2 Closed operators in Hilbert spaces -- 7.3 Bounded operators -- 7.4 Pure tensors versus pure state operators -- 7.5 Trace class operators -- 7.6 Hilbert-Schmidt operators -- 7.7 Compact operators -- References -- 8 Spaces and algebras for quantum operators. , 8.1 Banach and Hilbert space rank, boundedness, and Schauder bases -- 8.2 Commutative and noncommutative Banach algebras -- 8.3 Subgroup in a Banach algebra -- 8.4 Bounded operators on a Hilbert space -- 8.5 Invertible operator algebra criteria on a Hilbert space -- 8.6 Spectrum in a Banach algebra -- 8.7 Ideals in a Banach algebra -- 8.8 Gelfand-Naimark-Segal construction -- 8.9 Generating a C* algebra -- 8.10 The Gelfand formula -- References -- 9 Von Neumann algebra -- 9.1 Operator topologies -- 9.2 Two basic von Neumann algebras -- 9.3 Commutant in a von Neumann algebra -- 9.4 The Gelfand transform -- References -- 10 Fiber bundles -- 10.1 MSA for the algebraic quotient spaces -- 10.2 The topological quotient space -- 10.3 Basic topological and manifold concepts -- 10.4 Fiber bundles from manifolds -- 10.5 Sections in a fiber bundle -- 10.6 Line and vector bundles -- 10.7 Analytic vector bundles -- 10.8 Elliptic curves over C -- 10.9 The quaternions -- 10.10 Hopf fibrations -- 10.11 Hopf fibration with bloch sphere S2, the one-qubit base -- 10.12 Hopf fibration with sphere S4, the two-qubit base -- References -- 11 Lie algebras and Lie groups -- 11.1 Algebraic structure -- 11.2 MSA view of a Lie algebra -- 11.3 Dimension of a Lie algebra -- 11.4 Ideals in a Lie algebra -- 11.5 Representations and MSA of a Lie group of a Lie algebra -- 11.6 Briefing on topological manifold properties of a Lie group -- 11.7 Formal description of matrix Lie groups -- 11.8 Mappings between Lie groups and Lie algebras -- 11.9 Complexification of Lie algebras -- References -- 12 Fundamental and universal covering groups -- 12.1 Homotopy a graphical view -- 12.2 Initial point equivalence for loops -- 12.3 MSA description of the fundamental group -- 12.4 Illustrating the fundamental group -- 12.5 Homotopic equivalence for topological spaces. , 12.6 The universal covering group -- 12.7 The Cornwell mapping -- References -- 13 Spectra for operators -- 13.1 Spectral classification for bounded operators -- 13.2 Spectra for operators on a Banach space -- 13.3 Symmetric, self-adjoint, and unbounded operators -- 13.4 Bounded operators and numerical range -- 13.5 Self-adjoint operators -- 13.6 Normal operators and nonbounded operators -- 13.7 Spectral decomposition -- 13.8 Spectra for self-adjoint, normal, and compact operators -- 13.9 Pure states and density functions -- 13.10 Spectrum and resolvent set -- 13.11 Spectrum for nonbounded operators -- 13.12 Brief descriptions of spectral measures and spectral theorems -- References -- 14 Canonical commutation relations -- 14.1 Isometries and unitary operations -- 14.2 Canonical hypergroups-a multisorted algebra view -- 14.3 Partial isometries -- 14.4 Multisorted algebra for partial isometries -- 14.5 Stone's theorem -- 14.6 Position and momentum -- 14.7 The Weyl form of the canonical commutation relations and the Heisenberg group -- 14.8 Stone-von Neumann and quantum mechanics equivalence -- 14.9 Symplectic vector space-a multisorted algebra approach -- 14.10 The Weyl canonical commutation relations C& -- lowast -- algebra -- References -- 15 Fock space -- 15.1 Particles within Fock spaces and Fock space structure -- 15.2 The bosonic occupation numbers and the ladder operators -- 15.3 The fermionic Fock space and the fermionic ladder operators -- 15.4 The Slater determinant and the complex Clifford space -- 15.5 Maya diagrams -- 15.6 Maya diagram representation of fermionic Fock space -- 15.7 Young diagrams representing quantum particles -- 15.8 Bogoliubov transform -- 15.9 Parafermionic and parabosonic spaces -- 15.10 Segal-Bargmann-Fock operations -- 15.11 Many-body systems and the Landau many-body expansion -- 15.12 Single-body operations. , 15.13 Two-body operations -- References -- 16 Underlying theory for quantum computing -- 16.1 Quantum computing and quantum circuits -- 16.2 Single-qubit quantum gates -- 16.3 Pauli rotational operators -- 16.4 Multiple-qubit input gates -- 16.5 The swapping operation -- 16.6 Universal quantum gate set -- 16.7 The Haar measure -- 16.8 Solovay-Kitaev theorem -- 16.9 Quantum Fourier transform and phase estimation -- 16.10 Uniform superposition and amplitude amplification -- 16.11 Reflections -- References -- 17 Quantum computing applications -- 17.1 Deutsch problem description -- 17.2 Oracle for Deutsch problem solution -- 17.3 Quantum solution to Deutsch problem -- 17.4 Deutsch-Jozsa problem description -- 17.5 Quantum solution for the Deutsch-Jozsa problem -- 17.6 Grover search problem -- 17.7 Solution to the Grover search problem -- 17.8 The Shor's cryptography problem from an algebraic view -- 17.9 Solution to the Shor's problem -- 17.10 Elliptic curve cryptography -- 17.11 MSA of elliptic curve over a finite field -- 17.12 Diffie-Hellman EEC key exchange -- References -- Further reading -- 18 Machine learning and data mining -- 18.1 Quantum machine learning applications -- 18.2 Learning types and data structures -- 18.3 Probably approximately correct learning and Vapnik-Chervonenkis dimension -- 18.4 Regression -- 18.5 K-nearest neighbor classification -- 18.6 K-nearest neighbor regression -- 18.7 Quantum K-means applications -- 18.8 Support vector classifiers -- 18.9 Kernel methods -- 18.10 Radial basis function kernel -- 18.11 Bound matrices -- 18.12 Convolutional neural networks and quantum convolutional neural networks -- References -- 19 Reproducing kernel and other Hilbert spaces -- 19.1 Algebraic solution to harmonic oscillator -- 19.2 Reproducing kernel Hilbert space over C and the disk algebra. , 19.3 Reproducing kernel Hilbert space over R.

Note: Intro -- Advance Praise -- Title Page -- Rights Page -- Dedication -- Contents -- Acknowledgments -- Preface -- Introduction -- Part One: Compass for Change -- Chapter 1: Introducing and Using the Natural Step Framework -- Chapter 2: Sustainability: The Trouble We Have Talking About It -- Chapter 3: The Natural Step Approach: Why Is It Useful? -- Part Two: Practices that Changed -- Chapter 4: The Eco-municipalities of Sweden: A Little Background -- Chapter 5: Changing to Renewable Energy Sources -- Chapter 6: Getting Away from Fossil-fueled Vehicles: Transportation and Mobility -- Chapter 7: Ecological Housing -- Chapter 8: Green Businesses -- Green Buildings -- Chapter 9: Journeys to Self-sufficiency: Community Eco-economic Development -- Chapter 10: Ecological Schools -- Ecological Education -- Chapter 11: Sustainable Agriculture: Growing Healthy -- Growing Locally -- Chapter 12: Dealing with Waste -- Chapter 13: Natural Resources: Protecting Biodiversity -- Chapter 14: Sustainable Land Use and Planning -- Part Three: How Communities Can Change -- Chapter 15: What Gets in the Way of Change? -- Chapter 16: Three Change Processes That Work -- Chapter 17: Steps to Change -- Chapter 18: Inside the Head of a Process Leader -- Epi logue -- Appendix A: Location Map -- Appendix B: Guide to Swedish Name Pronunciation -- Appendix C: National Association of Swedish Ecomunicipalities (SeKom) Members in 2002 -- References and Sources -- Endnotes -- Index -- About the Authors.

Note: Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Convexity, colours and statistics -- 1.1 Convex sets -- 1.2 High-dimensional geometry -- 1.3 Colour theory -- 1.4 What is 'distance'? -- 1.5 Probability and statistics -- Problems -- 2 Geometry of probability distributions -- 2.1 Majorization and partial order -- 2.2 Shannon entropy -- 2.3 Relative entropy -- 2.4 Continuous distributions and measures -- 2.5 Statistical geometry and the Fisher-Rao metric -- 2.6 Classical ensembles -- 2.7 Generalized entropies -- Problems -- 3 Much ado about spheres -- 3.1 Spheres -- 3.2 Parallel transport and statistical geometry -- 3.3 Complex, Hermitian and Kähler manifolds -- 3.4 Symplectic manifolds -- 3.5 The Hopf fibration of the 3-sphere -- 3.6 Fibre bundles and their connections -- 3.7 The 3-sphere as a group -- 3.8 Cosets and all that -- Problems -- 4 Complex projective spaces -- 4.1 From art to mathematics -- 4.2 Complex projective geometry -- 4.3 Complex curves, quadrics and the Segre embedding -- 4.4 Stars, spinors and complex curves -- 4.5 The Fubini-Study metric -- 4.6 CP illustrated -- 4.7 Symplectic geometry and the Fubini-Study measure -- 4.8 Fibre bundle aspects -- 4.9 Grassmannians and flag manifolds -- Problems -- 5 Outline of quantum mechanics -- 5.1 Quantum mechanics -- 5.2 Qubits and Bloch spheres -- 5.3 The statistical and the Fubini-Study distances -- 5.4 A real look at quantum dynamics -- 5.5 Time reversals -- 5.6 Classical and quantum states: a unified approach -- Problem -- 6 Coherent states and group actions -- 6.1 Canonical coherent states -- 6.2 Quasi-probability distributions on the plane -- 6.3 Bloch coherent states -- 6.4 From complex curves to SU(K) coherent states -- 6.5 SU(3) coherent states -- Problems -- 7 The stellar representation -- 7.1 The stellar representation in quantum mechanics. , 7.2 Orbits and coherent states -- 7.3 The Husimi function -- 7.4 Wehrl entropy and the Lieb conjecture -- 7.5 Generalized Wehrl entropies -- 7.6 Random pure states -- 7.7 From the transport problem to the Monge distance -- Problems -- 8 The space of density matrices -- 8.1 Hilbert-Schmidt space and positive operators -- 8.2 The set of mixed states -- 8.3 Unitary transformations -- 8.4 The space of density matrices as a convex set -- 8.5 Stratification -- 8.6 An algebraic afterthought -- 8.7 Summary -- Problems -- 9 Purification of mixed quantum states -- 9.1 Tensor products and state reduction -- 9.2 The Schmidt decomposition -- 9.3 State purification and the Hilbert-Schmidt bundle -- 9.4 A first look at the Bures metric -- 9.5 Bures geometry for N = 2 -- 9.6 Further properties of the Bures metric -- Problems -- 10 Quantum operations -- 10.1 Measurements and POVMs -- 10.2 Algebraic detour: matrix reshaping and reshuffling -- 10.3 Positive and completely positive maps -- 10.4 Environmental representations -- 10.5 Some spectral properties -- 10.6 Unital and bistochastic maps -- 10.7 One qubit maps -- Problems -- 11 Duality: maps versus states -- 11.1 Positive and decomposable maps -- 11.2 Dual cones and super-positive maps -- 11.3 Jamiolkowski isomorphism -- 11.4 Quantum maps and quantum states -- Problems -- 12 Density matrices and entropies -- 12.1 Ordering operators -- 12.2 Von Neumann entropy -- 12.3 Quantum relative entropy -- 12.4 Other entropies -- 12.5 Majorization of density matrices -- 12.6 Entropy dynamics -- Problems -- 13 Distinguishability measures -- 13.1 Classical distinguishability measures -- 13.2 Quantum distinguishability measures -- 13.3 Fidelity and statistical distance -- Problems -- 14 Monotone metrics and measures -- 14.1 Monotone metrics -- 14.2 Product measures and flag manifolds -- 14.3 Hilbert-Schmidt measure. , 14.4 Bures measure -- 14.5 Induced measures -- 14.6 Random density matrices -- 14.7 Random operations -- Problems -- 15 Quantum entanglement -- 15.1 Introducing entanglement -- 15.2 Two qubit pure states: entanglement illustrated -- 15.3 Pure states of a bipartite system -- 15.4 Mixed states and separability -- 15.5 Geometry of the set of separable states -- 15.6 Entanglement measures -- I. Geometric measures -- II. Extensions of pure-state measures -- III. Operational measures -- IV. Algebraic measures -- 15.7 Two-qubit mixed states -- Problems -- Epilogue -- Appendix 1 Basic notions of differential geometry -- A1.1 Differential forms -- A1.2 Riemannian curvature -- A1.3 A key fact about mappings -- Appendix 2 Basic notions of group theory -- A2.1 Lie groups and Lie algebras -- A2.2 SU(2) -- A2.3 SU(N) -- A2.4 Homomorphisms between low-dimensional groups -- Appendix 3 Geometry: do it yourself -- Appendix 4 Hints and answers to the exercises -- References -- Index.

Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface to the first edition -- Preface to the second edition -- 1 · Quantum physics -- Light waves -- Photons -- The Heisenberg uncertainty principle -- Atoms and matter waves -- Beyond the atom -- Condensed matter -- 2 · Which way are the photons pointing? -- The polarisation of light -- The polarisation of photons -- Hidden variables -- 3 · What can be hidden in a pair of photons? -- Bell's theorem -- The experiments -- Discussion -- 4 · Wonderful Copenhagen? -- Copenhagen and EPR -- The measurement problem -- Schrödinger's cat -- 5 · Is it all in the mind? -- Quantum physics and reductionism -- 6 · Many worlds -- 7 · Is it a matter of size? -- Superconductivity -- 8 · Backwards and forwards -- Indelible records -- Irreversibility -- Irreversibility and measurement -- 9 · Only one way forward? -- Return to the measurement problem -- 10 · Can we be consistent? -- Actualisation -- 11 · Illusion or reality? -- Further reading -- General bibliography -- Specific bibliography -- 1 · Quantum physics -- 2 · Which way are the photons pointing? -- 3 · What can be hidden in a pair of photons? -- 5 · Is it all in the mind? -- 6 · Many worlds -- 7 · Is it a matter of size? -- 8 · Backwards and forwards -- 9 · Only one way forward? -- 10 · Can we be consistent? -- Index.

Note: BOOK COVER -- TITLE -- COPYRIGHT -- CONTENTS.

Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgments -- Part I From classical to wave mechanics -- 1 Experimental foundations of quantum theory -- 1.1 The need for a quantum theory -- 1.2 Our path towards quantum theory -- 1.3 Photoelectric effect -- 1.4 Compton effect -- 1.4.1 Thomson scattering -- 1.5 Interference experiments -- 1.6 Atomic spectra and the Bohr hypotheses -- 1.7 The experiment of Franck and Hertz -- 1.8 Wave-like behaviour and the Bragg experiment -- 1.9 The experiment of Davisson and Germer -- 1.10 Position and velocity of an electron -- 1.11 Problems -- Appendix 1.A The phase 1-form -- 2 Classical dynamics -- 2.1 Poisson brackets -- 2.2 Symplectic geometry -- 2.3 Generating functions of canonical transformations -- 2.3.1 Time-dependent Hamiltonian formalism -- 2.3.2 Dynamical time -- 2.3.3 Various generating functions -- 2.3.4 An example: particle in a repulsive potential -- 2.3.5 The harmonic oscillator -- 2.4 Hamilton and Hamilton-Jacobi equations -- 2.5 The Hamilton principal function -- 2.5.1 Free particle on a line -- 2.5.2 One-dimensional harmonic oscillator -- 2.5.3 Time-dependent Hamiltonian -- 2.6 The characteristic function -- 2.6.1 Principal versus characteristic function -- 2.7 Hamilton equations associated with metric tensors -- 2.8 Introduction to geometrical optics -- 2.8.1 Variational principles -- 2.9 Problems -- Appendix 2.A Vector fields -- Appendix 2.B Lie algebras and basic group theory -- Groups and sub-groups -- The general linear group GL(n,R) -- Euclidean and rotation group -- Galilei group -- Lorentz and Poincaré groups -- Unitary group -- Appendix 2.C Some basic geometrical operations -- Appendix 2.D Space-time -- Appendix 2.E From Newton to Euler-Lagrange -- 3 Wave equations -- 3.1 The wave equation -- 3.2 Cauchy problem for the wave equation. , 3.3 Fundamental solutions -- 3.3.1 Wave equations in spherical polar coordinates -- 3.4 Symmetries of wave equations -- 3.5 Wave packets -- 3.6 Fourier analysis and dispersion relations -- 3.6.1 The symbol of difierential operators -- 3.6.2 Dispersion relations -- 3.7 Geometrical optics from the wave equation -- 3.8 Phase and group velocity -- 3.9 The Helmholtz equation -- 3.10 Eikonal approximation for the scalar wave equation -- 3.11 Problems -- 4 Wave mechanics -- 4.1 From classical to wave mechanics -- 4.1.1 Continuity equation -- 4.1.2 Physical interpretation of the wave function -- 4.1.3 Mean values -- 4.1.4 Eigenstates and eigenvalues -- 4.2 Uncertainty relations for position and momentum -- 4.2.1 Uncertainty relations in relativistic systems -- 4.3 Transformation properties of wave functions -- 4.3.1 Direct approach to the transformation properties of the Schrödinger equation -- 4.3.2 Width of the wave packet -- 4.4 Green kernel of the Schrödinger equation -- 4.4.1 Free particle -- 4.5 Example of isometric non-unitary operator -- 4.6 Boundary conditions -- 4.6.1 Particle confined by a potential -- 4.6.2 Improper eigenfunctions -- 4.7 Harmonic oscillator -- 4.7.1 One-dimensional oscillator -- 4.7.2 Hermite polynomials -- 4.8 JWKB solutions of the Schrödinger equation -- 4.8.1 On the meaning of semi-classical -- 4.8.2 Example: alpha-decay -- 4.9 From wave mechanics to Bohr-Sommerfeld -- 4.9.1 Quantization of Keplerian motion -- 4.9.2 Harmonic oscillator -- 4.9.3 Rotator in a plane -- 4.10 Problems -- Appendix 4.A Glossary of functional analysis -- Appendix 4.B JWKB approximation -- Appendix 4.C Asymptotic expansions -- 5 Applications of wave mechanics -- 5.1 Reflection and transmission -- 5.2 Step-like potential: tunnelling effect -- 5.2.1 Step-like potential -- 5.2.2 Tunnelling effect -- 5.3 Linear potential. , 5.4 The Schrödinger equation in a central potential -- 5.5 Hydrogen atom -- 5.5.1 A simpler derivation of the Balmer formula -- 5.6 Introduction to angular momentum -- 5.6.1 Lie algebra of O(3) and associated vector fields -- 5.6.2 Quantum definition of angular momentum -- 5.6.3 Harmonic polynomials and spherical harmonics -- 5.6.4 Back to central potentials in R -- 5.7 Homomorphism between SU(2) and SO(3) -- 5.8 Energy bands with periodic potentials -- 5.9 Problems -- Appendix 5.A Stationary phase method -- Appendix 5.B Bessel functions -- 6 Introduction to spin -- 6.1 Stern-Gerlach experiment and electron spin -- 6.2 Wave functions with spin -- 6.2.1 Addition of orbital and spin angular momentum -- 6.3 The Pauli equation -- 6.4 Solutions of the Pauli equation -- 6.5 Landau levels -- 6.6 Problems -- Appendix 6.A Lagrangian of a charged particle -- Appendix 6.B Charged particle in a monopole field -- 7 Perturbation theory -- 7.1 Approximate methods for stationary states -- 7.1.1 Rayleigh-Schrödinger expansion -- 7.1.2 Brillouin-Wigner expansion -- 7.1.3 Remark on quasi-stationary states -- 7.2 Very close levels -- 7.3 Anharmonic oscillator -- 7.4 Occurrence of degeneracy -- 7.5 Stark effect -- 7.6 Zeeman effect -- 7.7 Variational method -- 7.8 Time-dependent formalism -- 7.8.1 Harmonic perturbations -- 7.8.2 Fermi golden rule -- 7.9 Limiting cases of time-dependent theory -- 7.9.1 Adiabatic switch on and off of the perturbation -- 7.9.2 Perturbation suddenly switched on -- 7.10 The nature of perturbative series -- 7.10.1 Regular perturbation theory -- 7.10.2 Asymptotic perturbation theory -- 7.10.3 Spectral concentration -- 7.10.4 Singular perturbation theory -- 7.11 More about singular perturbations -- 7.11.1 The Harrell method -- 7.11.2 Extension to other singular potentials -- 7.11.3 Concluding remarks -- 7.12 Problems. , Appendix 7.A Convergence in the strong resolvent sense -- 8 Scattering theory -- 8.1 Aims and problems of scattering theory -- 8.2 Integral equation for scattering problems -- 8.3 The Born series and potentials of the Rollnik class -- 8.4 Partial wave expansion -- 8.5 The Levinson theorem -- 8.6 Scattering from singular potentials -- 8.7 Resonances -- 8.8 Separable potential model -- 8.9 Bound states in the completeness relationship -- 8.10 Excitable potential model -- 8.11 Unitarity of the Möller operator -- 8.12 Quantum decay and survival amplitude -- 8.12.1 Law of radioactive decay: Poisson distribution -- 8.12.2 Quantum decay transitions. The survival amplitude -- 8.12.3 Decay amplitude under a Lorentz transformation -- 8.12.4 Quantum mechanics in dual spaces -- 8.13 Problems -- Part II Weyl quantization and algebraic methods -- 9 Weyl quantization -- 9.1 The commutator in wave mechanics -- 9.2 Abstract version of the commutator -- 9.3 Canonical operators and the Wintner theorem -- 9.4 Canonical quantization of commutation relations -- 9.5 Weyl quantization and Weyl systems -- 9.5.1 Representations -- 9.5.2 Unitary equivalence -- 9.5.3 Weyl quantization -- 9.6 The Schrödinger picture -- 9.7 From Weyl systems to commutation relations -- 9.8 Heisenberg representation for temporal evolution -- 9.9 Generalized uncertainty relations -- 9.9.1 Time-energy uncertainty relation -- 9.10 Unitary operators and symplectic linear maps -- 9.10.1 Translations -- 9.10.2 Rotations -- 9.10.3 Harmonic oscillator -- 9.11 On the meaning of Weyl quantization -- 9.12 The basic postulates of quantum theory -- 9.12.1 Rigged Hilbert spaces -- Position and momentum operators -- 9.13 Problems -- 10 Harmonic oscillators and quantum optics -- 10.1 Algebraic formalism for harmonic oscillators -- 10.2 A thorough understanding of Landau levels -- 10.3 Coherent states. , 10.4 Weyl systems for coherent states -- 10.5 Two-photon coherent states -- 10.6 Problems -- 11 Angular momentum operators -- 11.1 Angular momentum: general formalism -- 11.1.1 Algebraic method for the spectrum -- 11.1.2 Representations -- 11.1.3 Hilbert space -- 11.2 Two-dimensional harmonic oscillator -- 11.2.1 Introduction of different bases -- 11.3 Rotations of angular momentum operators -- 11.4 Clebsch-Gordan coefficients and the Regge map -- 11.5 Postulates of quantum mechanics with spin -- 11.6 Spin and Weyl systems -- 11.7 Monopole harmonics -- 11.8 Problems -- 12 Algebraic methods for eigenvalue problems -- 12.1 Quasi-exactly solvable operators -- 12.2 Transformation operators for the hydrogen atom -- 12.3 Darboux maps: general framework -- 12.4 SU(1, 1) structures in a central potential -- 12.5 The Runge-Lenz vector -- 12.6 Problems -- 13 From densitymatrix to geometrical phases -- 13.1 The density matrix -- 13.2 Applications of the density matrix -- 13.3 Quantum entanglement -- 13.4 Hidden variables and the Bell inequalities -- 13.5 Entangled pairs of photons -- 13.6 Production of statistical mixtures -- 13.7 Pancharatnam and Berry phases -- 13.7.1 More concerning non-integrable phases -- 13.8 The Wigner theorem and symmetries -- 13.9 A modern perspective on the Wigner theorem -- 13.10 Problems -- Part III Selected topics -- 14 From classical to quantum statistical mechanics -- 14.1 Aims and main assumptions -- 14.2 Canonical ensemble -- 14.3 Microcanonical ensemble -- 14.4 Partition function -- 14.5 Equipartition of energy -- 14.6 Specific heats of gases and solids -- 14.7 Black-body radiation -- 14.7.1 The Kirchhoff laws -- 14.7.2 Stefan and displacement laws -- 14.7.3 The Planck model -- 14.7.4 The contributions of Einstein -- 14.7.5 Dynamic equilibrium of the radiation field -- 14.8 Quantum models of specific heats. , 14.9 Identical particles in quantum mechanics.

Note: Front Cover -- Introduction to Quantum Mechanics: In Chemistry, Materials Science and Biology -- Copyright Page -- Table of Contents -- Preface -- About the Author -- Chapter 1. Atoms and Photons -- 1.1 Atomic and Subatomic Particles -- 1.2 Electromagnetic Waves -- 1.3 Three Failures of Classical Physics -- 1.4 Blackbody Radiation -- 1.5 The Photoelectric Effect -- 1.6 Line Spectra -- 1A. Supplement: Maxwell's Equations -- 1B. Supplement: Planck Radiation Law -- Chapter 2. Waves and Particles -- 2.1 Double-Slit Experiment -- 2.2 Wave-Particle Duality -- 2.3 The Schrödinger Equation -- 2.4 Operators and Eigenvalues -- 2.5 The Wavefunction -- Problems -- Chapter 3. Quantum Mechanics of Some Simple Systems -- 3.1 The Free Particle -- 3.2 Particle in a Box -- 3.3 Free-Electron Model -- 3.4 Particle in a Three-Dimensional Box -- Problems -- Chapter 4. Principles of Quantum Mechanics -- 4.1 Hermitian Operators -- 4.2 Eigenvalues and Eigenfunctions -- 4.3 Expectation Values -- 4.4 More on Operators -- 4.5 Postulates of Quantum Mechanics -- 4.6 Dirac Bra-Ket Notation -- 4.7 The Variational Principle -- 4.8 Spectroscopic Transitions -- 4A. Supplement: Time-Dependent Perturbation Theory for Radiative Transitions -- Problems -- Chapter 5. The Harmonic Oscillator -- 5.1 Classical Oscillator -- 5.2 Quantum Harmonic Oscillator -- 5.3 Harmonic-Oscillator Eigenfunctions and Eigenvalues -- 5.4 Operator Formulation of Harmonic Oscillator -- 5.5 Quantum Theory of Radiation -- 5A. Supplement: Gaussian Integrals -- 5B. Supplement: Special Functions: Hermite Polynomials -- Problems -- Chapter 6. Angular Momentum -- 6.1 Particle in a Ring -- 6.2 Free-Electron Model for Aromatic Molecules -- 6.3 Spherical Polar Coordinates -- 6.4 Rotation in Three Dimensions -- 6.5 Theory of Angular Momentum -- 6.6 Electron Spin -- 6.7 Addition of Angular Momenta. , 6A. Supplement: Curvilinear Coordinates -- 6B. Supplement: Legendre Functions and Spherical Harmonics -- 6C. Supplement: Pauli Spin Algebra -- Chapter 7. The Hydrogen Atom and Atomic Orbitals -- 7.1 Atomic Spectra -- 7.2 The Bohr Atom -- 7.3 Quantum Mechanics of Hydrogenlike Atoms -- 7.4 Hydrogen-Atom Ground State -- 7.5 Atomic Orbitals -- 7.6 p- and d-Orbitals -- 7.7 Summary on Atomic Orbitals -- 7.8 Reduced Mass -- 7A. Supplement: Laguerre Polynomials -- Problems -- Chapter 8. Helium Atom -- 8.1 Experimental Energies -- 8.2 Schrödinger Equation and Variational Calculations -- 8.3 Spinorbitals and the Exclusion Principle -- 8.4 Excited States of Helium -- Problems -- Chapter 9. Atomic Structure and the Periodic Law -- 9.1 Pauli Exclusion Principle and Slater Determinants -- 9.2 Aufbau Principles -- 9.3 Atomic Configurations and Term Symbols -- 9.4 Periodicity of Atomic Properties -- 9.5 Relativistic Effects -- 9.6 Spiral Form of the Periodic Table -- 9.7 Hartree Self-Consistent Field (SCF) Theory -- Problems -- Chapter 10. The Chemical Bond -- 10.1 The Hydrogen Molecule -- 10.2 Valence-Bond Theory -- 10.3 Hybrid Orbitals and Molecular Geometry -- 10.4 Hypervalent Compounds -- 10.5 Valence-Shell Model -- 10.6 Transition Metal Complexes -- 10.7 The Hydrogen Bond -- 10.8 Critique of Valence-Bond Theory -- Problems -- Chapter 11. Molecular Orbital Theory I. Diatomic Molecules -- 11.1 The Hydrogen Molecule-Ion -- 11.2 The LCAO Approximation -- 11.3 Molecular Orbital Theory of Homonuclear Diatomic Molecules -- 11.4 Variational Computations of Molecular Orbitals -- 11.5 Heteronuclear Molecules -- 11.6 Electronegativity -- Problems -- Chapter 12. Molecular Orbital Theory II. Polyatomic Molecules and Solids -- 12.1 Hückel Molecular Orbital Theory -- 12.2 Conservation of Orbital Symmetry: Woodward-Hoffmann Rules. , 12.3 Band Theory of Metals and Semiconductors -- 12.4 Computational Chemistry -- 12.5 Density Functional Theory -- Problems -- Chapter 13. Molecular Symmetry -- 13.1 The Ammonia Molecule -- 13.2 Mathematical Theory of Groups -- 13.3 Group Theory in Quantum Mechanics -- 13.4 Molecular Orbitals for Ammonia -- 13.5 Selection Rules -- 13.6 The Water Molecule -- 13.7 Walsh Diagrams -- 13.8 Molecular Symmetry Groups -- 13.9 Dipole Moments and Optical Activity -- 13.10 Character Tables -- Problems -- Chapter 14. Molecular Spectroscopy -- 14.1 Vibration of Diatomic Molecules -- 14.2 Vibration of Polyatomic Molecules -- 14.3 Rotation of Diatomic Molecules -- 14.4 Rotation-Vibration Spectra -- 14.5 Molecular Parameters from Spectroscopy -- 14.6 Rotation of Polyatomic Molecules -- 14.7 Electronic Excitations -- 14.8 Lasers -- 14.9 Raman Spectroscopy -- Problems -- Chapter 15. Nuclear Magnetic Resonance -- 15.1 Magnetic Properties of Nuclei -- 15.2 Nuclear Magnetic Resonance -- 15.3 The Chemical Shift -- 15.4 Spin-Spin Coupling -- 15.5 Mechanism for Spin-Spin Interactions -- 15.6 Magnetization and Relaxation Processes -- 15.7 Pulse Techniques and Fourier Transforms -- 15.8 Two-Dimensional NMR -- 15.9 Magnetic Resonance Imaging -- Problems -- Chapter 16. Wonders of the Quantum World -- 16.1 The Copenhagen Interpretation -- 16.2 Superposition -- 16.3 Schrödinger's Cat -- 16.4 Einstein-Podolsky-Rosen Experiment -- 16.5 Bell's Theorem -- 16.6 Aspect's Experiment -- 16.7 Multiple Photon Entanglement -- 16.8 Quantum Teleportation -- 16.9 Quantum Computers -- 16.10 Quantum Computing with NMR -- Problems -- Suggested References -- Answers to Problems -- Index -- Series Book.

Note: Front Cover -- Sustainable Resource Management -- Sustainable Resource Management: Modern Approaches and Contexts -- Copyright -- Dedication -- Contents -- Contributors -- Editors' biography -- Preface -- 1 - Evolution of the concept of sustainability. From Brundtland Report to sustainable development goals -- 1. Introduction -- 2. The concept of sustainable development -- 3. The definition of sustainable development -- 4. The trend of sustainable development -- 5. The evolution of sustainable development concept -- 6. Indicator development -- 7. Environmental sustainability -- 7.1 Social sustainability -- 7.2 Economic sustainable development -- 7.3 Context of sustainable development goals -- 7.4 Key Millennium Development Goal achievements -- 8. Sustainable development goals -- 8.1 Goal 1. End poverty everywhere in all of its forms -- 8.2 Goal 2. End hunger, achieve food security, improve nutrition, and promote sustainable agriculture -- 8.3 Goal 3. Ensure healthy lives and promote welfare for all people -- 8.4 Goal 4. Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all -- 8.5 Goal 5. Achieve gender equality and empower all women and girls -- 8.6 Goal 6. Ensure availability and sustainable management of water and sanitation for all -- 8.7 Goal 7. Ensure access to affordable, reliable, sustainable and modern energy for all -- 8.8 Goal 8. Promote sustained, inclusive, and sustainable economic growth, full and productive employment, and decent work for all -- 8.9 Goal 9. Build resilient infrastructure, promote inclusive and sustainable industrialization, and foster innovation -- 8.10 Goal 10. Reduce inequality within and among countries -- 8.11 Goal 11. Make cities and human settlements inclusive, safe, resilient, and sustainable -- 8.12 Goal 12. Ensure sustainable consumption and production patterns. , 8.13 Goal 13. Take urgent action to combat climate change and its impacts -- 8.14 Goal 14. Conserve and sustainably use oceans, seas, and marine resources for sustainable development -- 8.15 Goal 15. Protect, restore, and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desert ... -- 8.16 Goal 16. Promote peaceful and inclusive societies for sustainable development, provide access to justice for all, and build ... -- 8.17 Goal 17. Strengthen the means of implementation and revitalize the global partnership for sustainable development -- 8.17.1 Finance -- 8.17.2 Technology -- 8.17.3 Capacity-building -- 8.17.4 Trade -- 8.17.5 Systemic issues -- 8.18 Sustainable development goals and targets 2030 -- 9. Conclusions -- References -- Further reading -- 2 - Areas of sustainability: environment, economy, and society -- 1. Areas of sustainability: environment, economy, and society -- 1.1 Pillars of social responsibility-social, economic, and environmental -- 1.1.1 Social pillar -- 1.1.2 Economic pillar -- 1.1.3 Environmental pillar -- 1.1.4 Corporate philanthropy -- 1.2 Interconnections between economic growth, energy consumption, social welfare, and sustainable quality of life -- 1.3 Limitations of stable economic growth -- 1.3.1 Growth and the rules of arithmetic -- 1.3.2 Stable growth in a confined space -- 1.3.3 Economic growth, increase in population, and energy resources consumption increase -- 1.3.4 Natural and environmental limitations of economic growth -- 1.3.4.1 European criteria for sustainable forest management -- 1.3.5 Change of climate conditions-global warming -- 2. Conclusion -- References -- Further reading -- 3 - Evolution and trends of sustainable approaches -- 1. Introduction -- 2. Emergence of sustainable development. , 3. Approaches to sustainability assessment: sustainability indicators and assessment based on life cycles -- 3.1 Sustainability assessment and indicators -- 3.2 Sustainability assessment approach based on life cycles (LCSA) -- 3.2.1 Life cycle assessment -- 3.2.2 Social life cycle assessment -- 3.2.3 Life cycle costing -- 4. Approaches to sustainable solutions -- 4.1 Products, services, and technology -- 4.2 Sustainable business models -- 4.2.1 Product-service system -- 4.2.2 Circular economy -- 4.2.3 Industrial symbiosis -- 5. Conclusions -- References -- 4 - Modern age of sustainability: supply chain resource management -- 1. Introduction -- 2. Sustainable supply chain management -- 3. Practices for a greener and more sustainable supply chain -- 3.1 Design for sustainability -- 3.2 Eco-efficiency -- 3.3 Eco-design -- 3.4 Green purchasing -- 3.5 Reverse logistics -- 4. Sustainability evaluation methods -- 4.1 Full LCA -- 4.2 Direct life cycle assessment -- 4.3 Streamlined life cycle assessment -- 4.4 Environmental labeling -- 5. Conclusions -- References -- Other references of interest -- 5 - Sustainable management of agricultural resources (agricultural crops and animals) -- 1. Introduction -- 2. Sustainable management of agrobiodiversity -- 2.1 Biodiversity -- 2.2 Agrobiodiversity -- 2.2.1 Genetic agrobiodiversity -- 2.2.2 Specific agrobiodiversity -- 2.2.3 Ecosystem agrobiodiversity -- 2.2.4 Landscape agrobiogeodiversity -- 2.2.5 Loss of agrobiodiversity -- 2.2.6 Conservation of agrobiodiversity -- 3. Sustainable management of agricultural species -- 3.1 Agricultural plants (Crops) -- 3.2 Agricultural animals -- 3.2.1 Livestock biodiversity -- 4. Sustainable management of agroecosystems -- 4.1 Agroecology -- 4.2 Agroecosystems services -- 4.2.1 Agricultural crop services -- 4.2.2 Agricultural animals services -- 4.3 Agroecosystem health. , 4.4 Agroecosystems conservation -- 5. Sustainable management of agricultural landscapes -- 5.1 Agricultural landscape ecology -- 5.2 Sustainable management of agricultural landscapes -- 5.2.1 Agrolandscape services -- 5.2.2 Sustainable landscape management -- 6. Sustainable agriculture -- 6.1 Sustainable management of agricultural resources (sustainable management of crop and animal production) -- 6.1.1 Alternative agriculture -- 6.1.2 Intensive agriculture -- 6.1.3 Biodynamic agriculture -- 6.1.4 Ecological agriculture -- 6.1.5 Conservation agriculture -- 6.1.6 Organic agriculture -- 6.1.7 Permanent agriculture (permaculture) -- 6.1.8 Regenerative agriculture -- 6.1.9 Climate-smart agriculture -- 7. Sustainable rural development -- 7.1 Sustainable rural systems -- 7.1.1 Guidelines for sustainable rural systems -- 7.1.2 Sustainable crop production -- 7.1.2.1 Assessment and implementation of sustainable crop production -- 7.1.2.2 Sustainable crop production intensification -- 7.1.2.3 Sustainable crop production techniques -- 7.1.2.4 Sustainable management of crop nutrients -- 7.1.3 Sustainable animal production -- 7.1.3.1 Global agenda for sustainable livestock -- 7.1.3.2 Integrated crop-livestock production -- 7.2 Sustainable intensification of rural systems -- 7.2.1 Sustainable intensification of crop and animal production -- 7.2.1.1 Farming practices for sustainable intensification -- 8. Conclusions -- 8.1 The State of Food and Agriculture -- 8.2 The State of Food Security and Nutrition in the World -- 8.3 Industrialized agriculture -- 8.4 Holistic agriculture -- 8.5 Agrobiodiversity -- 8.6 Agroecosystems and Agrolandscapes -- 8.7 Sustainable agriculture -- 8.8 Sustainable rural systems -- 8.9 Landscape approaches for climate-smart agriculture -- 9. Metascientific approach to sustainable management of agricultural resources. , 10. Covid-19 pandemic impacts on agriculture, food security and nutrition -- 10.1 COVID-19 pandemic -- 10.2 COVID-19 pandemic impact on food and agriculture -- 10.3 COVID-19 pandemic development and solutions -- The FAO COVID-19 Response and Recovery Programme -- Acknowledgment -- References -- Internet links -- 6 - Sustainable water resources -- 1. Introduction -- 2. Water resource management system -- 3. Water resource management: an integrated approach -- 3.1 Historical background -- 3.2 Review of water resource management frameworks -- 3.3 Key issues for sustainable water management -- 4. Interventions of modern computation techniques for sustainable water management -- 4.1 Decision-making model approach -- 4.2 Agent-Based Modeling -- 4.3 Machine learning approach -- 5. Concluding remarks -- References -- Further reading -- 7 - Minerals and metal Industry in the global scenario and environmental sustainability -- 1. Introduction -- 2. The vision of this study -- 3. The vast scientific doctrine of environmental sustainability -- 4. Sustainable resource management, integrated water resource management, and the vast vision for the future -- 5. Today's mineral and metal industry and the needs of environmental sustainability -- 6. Recent scientific advancements in the field of environmental sustainability -- 7. Recent scientific prowess and research endeavor in the field of environmental sustainability, wastewater treatment, and min ... -- 8. Industrial wastewater treatment and mineral and metal industry -- 9. Heavy metal and arsenic groundwater remediation and the future of mineral and metal industry -- 10. Future scientific recommendations and the future flow of scientific thoughts -- 11. Conclusion, summary, and scientific perspectives -- References -- 8 - Sustainable land use and management -- 1. Introduction -- 2. Land uses and changes. , 3. Impacts of land use changes.