From particle in a box to PT -symmetric systems via isospectral deformation

Details From particle in a box to PT -symmetric systems via isospectral deformation From particle in a box to PT -symmetric systems via isospectral deformation

2011-10-17

arxiv.org/abs/1110.3708v3

Physics

Mathematical Physics

7 pages, 2 figures, figures have been updated and PACS numbers have been added, text have been updated with enhanced contents

Scientific paper

A family of PT -symmetric complex potentials are obtained which is isospectral to free particle in an infinite complex box in one dimension (1-D). These are generalizations to the cosec2(x) potential, isospectral to particle in a real infinite box. In the complex plane, the infinite box is extended parallel to the real axis having a real width, which is found to be an integral multiple of a constant quantum factor, arising due to boundary conditions necessary for maintaining the PT -symmetry of the superpartner. As the spectra of the particle in a box is still real, it necessarily picks out the unbroken PT -sector of its superpartner, thereby invoking a close relation between PT -symmetry and SUSY for this case.

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