Abstract
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 Schrodinger'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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