Re-establishing supersymmetry between harmonic oscillators in $D\ne 1$ dimensions

Abstract

Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials $V(q)=q^2+G/q^2+const$ and (b) many non-equivalent Hermitian and non-Hermitian (PT symmetric) systems may often be studied in parallel (with a schematic solvable illustrative example added).

arXiv commentWritten version of the review lecture presented during the winter school Geometry and Physics (Srni, Czech Republic, 12. - 19. January 2002), submitted to its proceedings. Latex, 13 pp, 2 figures

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