New types of solvability in PT symmetric quantum theory

Details New types of solvability in PT symmetric quantum theory New types of solvability in PT symmetric quantum theory

2005-01-22

arxiv.org/abs/math-ph/0501058v1

in "Superintegrability in Classical and Quantum Systems", Ed. P.Tempesta et al, CRM Proc. Lect. Notes 37, AMS, Providence, 200

Physics

Mathematical Physics

Workshop on Superintegrability in Classical and Quantum Systems, September 16-21, 2002, CRM Montreal, Canada, invited talk. 15

Scientific paper

The characteristic anti-linear (parity/time reversal, PT) symmetry of non-Hermitian Hamiltonians with real energies is presented as a source of two new forms of solvability of Schr\"{o}dinger's bound-state problems. In detail we describe (1) their very specific semi-exact solvability (SES) and (2) their innovated variational tractability. SES technicalities are discussed via charged oscillator example. In a broader context, speculations are added concerning possible relationship between PT symmetry, solvability and superintegrability.

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