Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

doi:10.1088/1674-1056/26/6/060301

中国物理B ›› 2017, Vol. 26 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/26/6/060301

Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

M Baradaran, H Panahi

Department of Physics, University of Guilan, Rasht 41635-1914, Iran

收稿日期:2016-11-18 修回日期:2017-02-09 出版日期:2017-06-05 发布日期:2017-06-05
通讯作者: H Panahi E-mail:t-panahi@guilan.ac.ir

Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

M Baradaran, H Panahi

Department of Physics, University of Guilan, Rasht 41635-1914, Iran

Received:2016-11-18 Revised:2017-02-09 Online:2017-06-05 Published:2017-06-05
Contact: H Panahi E-mail:t-panahi@guilan.ac.ir

摘要/Abstract

摘要： We use the Bethe ansatz method to investigate the Schrödinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl(2) hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl(2) Lie algebra. It is found that the results of the two methods are the same.

关键词: PT-symmetry, Bethe ansatz method, Lie algebraic approach, quasi-exactly solvable

Abstract: We use the Bethe ansatz method to investigate the Schrödinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl(2) hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl(2) Lie algebra. It is found that the results of the two methods are the same.

Key words: PT-symmetry, Bethe ansatz method, Lie algebraic approach, quasi-exactly solvable

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Db (Functional analytical methods) 03.65.Fd (Algebraic methods) 03.65.Ge (Solutions of wave equations: bound states)

M Baradaran,H Panahi. Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method[J]. 中国物理B, 2017, 26(6): 60301-060301.

M Baradaran, H Panahi. Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method[J]. Chin. Phys. B, 2017, 26(6): 60301-060301.

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Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

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