Non-Hermitian supersymmetry and singular PT symmetrized oscillators

Details Non-Hermitian supersymmetry and singular PT symmetrized oscillators Non-Hermitian supersymmetry and singular PT symmetrized oscillators

2002-01-09

arxiv.org/abs/hep-th/0201056v1

J.Phys.A35:2341-2352,2002

Physics

High Energy Physics

High Energy Physics - Theory

24 pages incl. 5 tables and 1 figure

Scientific paper

10.1088/0305-4470/35/9/320

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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