Note: Intro -- Preface -- Contents -- About the Author -- 1 Introduction -- 2 Systems of One or More Particles -- 2.1 One-Body System: A Particle in a Potential Field -- 2.2 Two-Body System with Mutual Interaction -- 2.2.1 Two Distinct Particles -- 2.2.2 Two Identical Particles: Symmetry of Wave Function -- 2.2.3 Inclusion of Spin Degrees of Freedom -- 2.2.4 Introduction of Isospin Degrees of Freedom for Nucleons -- 2.3 System of Several Particles -- 2.3.1 Independent Particle Model: Mean-Field Description -- 2.3.2 Many-Body Description -- References -- 3 Three-Body System -- 3.1 Jacobi Coordinates -- 3.2 Hyperspherical Harmonics -- 3.3 Schrödinger Equation for Relative Motion -- 3.4 Calculation of Potential Matrix Element -- 3.4.1 Expansion of potential in hyperspherical multipoles -- 3.4.2 Calculation of potential multipole -- 3.5 Symmetrization of HH Basis -- 3.6 Calculation of GSC for Central Potentials -- References -- 4 General Many-Body Systems -- 4.1 Jacobi Coordinates and Hyperspherical Variables -- 4.2 Generalized Hyperspherical Harmonics -- 4.3 Symmetrization of Wave Function -- 4.3.1 Kinematic Rotation Vector (KRV) -- 4.3.2 Symmetrization of Wave Function -- 4.4 Schrödinger Equation: Coupled Differential Equations -- 4.5 Approximation by Truncation of Basis -- 4.5.1 Restriction of Symmetry Components -- 4.5.2 Lm Approximation -- 4.5.3 Optimal Subset -- 4.5.4 Potential Harmonics -- 4.6 Truncation of Basis: Application to Particles and Nuclei -- 4.6.1 Baryons as Three-Quark Systems -- 4.6.2 Nuclear Few-Body Systems -- References -- 5 The Trinucleon System -- 5.1 Symmetrization of Spin--Isospin Wave Function -- 5.1.1 States Having Total Isospin t=12 and Spin s=12 -- 5.1.2 States Having Total Isospin t=32 and Spin s=12 -- 5.1.3 States Having Total Isospin t=12 and Spin s=32 -- 5.1.4 States Having Total Isospin t=32 and Spin s=32. , 5.2 Symmetrization of Total Wave Function -- 5.2.1 General Expression for Fully Antisymmetric Wave Function -- 5.2.2 Construction of HH for Different Partitions -- 5.3 Optimal Subset for the Trinucleon -- 5.4 Calculation of Potential Matrix Element: GSC -- 5.4.1 Coupling Among S and S' States Through Central interactions -- 5.4.2 Coupling Between S and D State Through Tensor Interaction -- 5.4.3 Coupling Between S' and D States Through Tensor Interaction -- 5.4.4 Coupling Between Two D States Through Central Forces -- 5.4.5 Coupling Between Two D States Through Tensor Interaction -- 5.4.6 Numerical Computation of GSCs -- 5.5 Results of Numerical Calculations for 3H and 3He -- 5.6 Addition of Three-Nucleon Forces -- References -- 6 Application to Coulomb Systems -- 6.1 Two-Electron Atoms -- 6.1.1 Exact Non-adiabatic Treatment of Two-Electron Atoms -- 6.1.2 Convergence of HH Expansion: Extrapolation and Accuracy -- 6.2 General Three-Body Coulomb Bound Systems -- 6.2.1 Adiabatic Approximation in Coulomb Systems -- References -- 7 Potential Harmonics -- 7.1 Potential Harmonics -- 7.2 Potential Multipoles -- 7.3 Overlap of PHs of Different Pairs -- 7.4 Potential Basis as Optimal Subset -- 7.4.1 Symmetrical PH Basis -- 7.5 Potential Matrix in Unsymmetrized PH Basis -- References -- 8 Application to Bose--Einstein Condensates -- 8.1 General Properties of BEC -- 8.2 GP Equation -- 8.2.1 Simplifying Assumptions and Their Limitations -- 8.2.2 Rigorous Proof of Existence of BEC and Derivation of the GP Equation -- 8.3 Many-Body Approach -- 8.4 Need for a Short-Range Correlation Function -- 8.5 Results for Repulsive and Attractive Condensates -- References -- 9 Integro-Differential Equation -- 9.1 Derivation of IDE -- 9.2 Applications of IDE -- 9.2.1 Nuclear Systems -- 9.2.2 Bose--Einstein Condensates -- References -- 10 Computational Techniques. , 10.1 Solution of a Single Differential Equation -- 10.2 Solution of Coupled Differential Equations -- 10.2.1 Exact Solution of the CDE -- 10.2.2 Introduction of Hypercentral Average -- 10.2.3 Hyperspherical Adiabatic Approximation -- 10.3 Computation of Matrix Element -- References -- Index.