New types of solvability in PT symmetric quantum theory

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. PT symmetric quantum mechanics: A brief introduction Prehistory: Isospectral operators. Origins of the popular Bender’s and Boettcher’s PT symmetric quantum mechanics [B0, B2] lie in perturbation theory [CG, FG]. For an elementary illustration one may recollect the pioneering paper by Buslaev and Grecchi [BG] who proved the isospectrality of the Hermitian, spherically symmetric D−dimensional perturbed harmonic oscillator H(g) = 1 2 