2005/01/22 by Miloslav Znojil
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:81Q05 #msc:34M25 #msc:35Q40 #msc:46C20
published as in "Superintegrability in Classical and Quantum Systems", Ed. P.Tempesta et al, CRM Proc. Lect. Notes 37, AMS, Providence, 2004 · Workshop on Superintegrability in Classical and Quantum Systems, September 16-21, 2002, CRM Montreal, Canada, invited talk. 15 pp
arxiv created 2005/01/22 · arxiv updated 2009/12/01
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 Schrödinger'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.