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arXiv · 1101.1040

Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator

Bikashkali Midya·Partha Pratim Dube·Rajkumar Roychoudhury
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Abstract

The generalized Swanson Hamiltonian $H_{GS} = w (\tilde{a}\tilde{a}^\dag+ 1/2) + \alpha \tilde{a}^2 + \beta \tilde{a}^{\dag^2}$ with $\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\tilde{a},\tilde{a}^\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\tilde{a}$ and $\tilde{a}^\dag$ is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason for this anomaly is discussed in the frame work of position dependent mass models by choosing $A(x)$ as the inverse square root of the mass function.

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Bikashkali Midya, Partha Pratim Dube, Rajkumar Roychoudhury. 2011-01-05. Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator. https://doi.org/10.1088/1751-8113/44/6/062001

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