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Non-Hermitian supersymmetry and singular PT symmetrized oscillators

Miloslav Znojil
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Abstract

SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called PT symmetric) quantum mechanics we show how SUSY between strongly singular harmonic oscillators can completely be re-established. Our recipe leads to a new form of the bosonic creation and annihilation operators and proves continuous near the usual regular (i.e., linear harmonic) limit.

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Miloslav Znojil. 2002-01-09. Non-Hermitian supersymmetry and singular PT symmetrized oscillators. https://doi.org/10.1088/0305-4470%2F35%2F9%2F320

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