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arXiv · 0909.3664

Equivalent Hermitian operator from supersymmetric quantum mechanics

Boris F. Samsonov·V. V. Shamshutdinova·A. V. Osipov
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Abstract

Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $η$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $η$ operators. We show that despite the fact that an $η$ operator produced by a supersymmetric transformation, corresponding to the exact supersymmetry, is singular, it can be used to find the eigenfunctions of a Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once the eigenfunctions of the Hermitian operator are found the operator may be reconstructed with the help of the spectral decomposition.

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Boris F. Samsonov, V. V. Shamshutdinova, A. V. Osipov. 2010-04-08. Equivalent Hermitian operator from supersymmetric quantum mechanics. https://doi.org/10.1016/j.physleta.2010.02.061

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