A Sinha and P Roy 2008 J. Phys. A: Math. Theor. 41 335306 doi:10.1088/1751-8113/41/33/335306
Pseudo supersymmetric partners for the generalized Swanson model
A Sinha and P Roy
Show affiliationsNew non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., 
, where α, β are real constants, with α ≠ β, and 
and 
are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H−, and its partner H+, are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians H±, related to their respective Hermitian counterparts h±, through the same similarity transformation operator ρ:H± = ρ−1h±ρ. The formalism is applied to the entire class of shape-invariant models.
- PACS
- MSC
-
81Q60 Supersymmetric quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
- Subjects
- Dates
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Issue 33 (22 August 2008)
Received 24 March 2008, in final form 18 June 2008
Published 22 July 2008
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Pseudo supersymmetric partners for the generalized Swanson model
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