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

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

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.

Keywords: PT-symmetry Bethe ansatz method Lie algebraic approach quasi-exactly solvable

Received: 18 November 2016
Revised: 09 February 2017
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	03.65.Db	(Functional analytical methods)
	03.65.Fd	(Algebraic methods)
	03.65.Ge	(Solutions of wave equations: bound states)

Corresponding Authors: H Panahi
E-mail: t-panahi@guilan.ac.ir

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M Baradaran, H Panahi Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method 2017 Chin. Phys. B 26 060301

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

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