Non-Hermitian supersymmetry and singular, 𝒫𝒯-symmetrized oscillators

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.

Identifiers

DOI

10.1088/0305-4470/35/9/320

Citations and references