New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization

被引:8
|
作者
Bagchi, Bijan [1 ]
Marquette, Ian [2 ]
机构
[1] Univ Calcutta, Dept Appl Math, Kolkata 700009, India
[2] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia
基金
澳大利亚研究理事会;
关键词
Schrodinger equation; Supersymmetry; Swanson oscillator; Superintegrability; Pseudo-Henniticity; PT-symmetry; POTENTIALS; SUPERSYMMETRY;
D O I
10.1016/j.physleta.2015.04.009
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We derive a one-step extension of the well known Swanson oscillator that describes a specific type of pseudo-Hermitian quadratic Hamiltonian connected to an extended harmonic oscillator model. Our analysis is based on the use of the techniques of supersymmetric quantum mechanics and addresses various representations of the ladder operators starting from a seed solution of the harmonic oscillator expressed in terms of a pseudo-Hermite polynomial. The role of the resulting chain of Hamiltonians related to similarity transformation is then exploited. In the second part we write down a two dimensional generalization of the Swanson Hamiltonian and establish superintegrability of such a system. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:1584 / 1588
页数:5
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