In:
Journal of Mathematical Physics, AIP Publishing, Vol. 57, No. 12 ( 2016-12-01)
Abstract:
We propose a unified approach to exactly diagonalize generalized non-Hermitian so(3,2) models. This approach is a series of similarity transformations, which is constructed by some similarity transformation operators associated with su(1,1) and su(2) subalgebras of so(3,2) Lie algebra. During this diagonalization, it is worth noting that a key step is to get rid of the terms Eˆ± and Fˆ± together via the proper similarity transformations first. In this way, exact solutions of the non-Hermitian so(3,2) models are obtained. Meanwhile we give the corresponding eigenstates, which are regarded as Lie algebra so(3,2) coherent-like number states. The results can cover the generic form of the eigenvalues and eigenstates to the generalized non-Hermitian two-mode boson systems with the discrete spectrum, including 2D PT-symmetric and non-PT-symmetric oscillators as the special cases. Also they are true for the Hermitian case.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
2016
detail.hit.zdb_id:
1472481-9
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