Non-Hermitian supersymmetry and singular PT symmetrized oscillators
Miloslav Znojil
TL;DR
This paper demonstrates how supersymmetry can be restored in singular, PT-symmetric quantum oscillators through regularization, leading to new operators and a smooth transition to regular harmonic oscillators.
Contribution
It introduces a novel method to re-establish SUSY in singular PT-symmetric oscillators, including new creation and annihilation operators that connect to regular harmonic oscillators.
Findings
SUSY can be fully restored in singular PT-symmetric oscillators.
New bosonic operators are derived that maintain continuity with regular oscillators.
The approach provides a consistent framework for singular potentials in PT-symmetric quantum mechanics.
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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