Equivalent Hermitian operator from supersymmetric quantum mechanics

Details Equivalent Hermitian operator from supersymmetric quantum mechanics Equivalent Hermitian operator from supersymmetric quantum mechanics

2009-09-21

arxiv.org/abs/0909.3664v2

Phys.Lett.A374:1962-1965,2010

Physics

Mathematical Physics

9 pages; revised formula (14), published version with erratum

Scientific paper

10.1016/j.physleta.2010.02.061

Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $\eta$ operators. We show that despite the fact that an $\eta$ 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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