Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
| Autor: | Ye��ilta��, ��zlem |
|---|---|
| Rok vydání: | 2011 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1108.0106 |
| Popis: | Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian $H_{-}=��(��^��� ��+\1/2)+����^{2}+����^{���2}$, where $��\neq ��$ and $��$ is a first order differential operator, to obtain the partner potentials $V_{+}(x)$ and $V_{-}(x)$ which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians $H_{\pm}$. We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of $V_{-}(x)$ which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked that if the intertwining operator satisfies $��_{1} H_{-}=H_{+} ��_{1}$, where $��_{1}=��^{-1} \mathcal{A} ��$ and $\mathcal{A}$ is the first order differential operator, which factorizes Hermitian equivalents of $H_{\pm}$. 11 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|