Abstract
For a fixed real energy, we prove that the classical turning points of a complex PT-symmetric potential occur as (z, -z*): either as (−a +ib, a + ib) or as ic. It is only in the former case that the potential possesses real discrete spectrum. The phase-space trajectories are closed and segregated in two parts: real (x, preal) and imaginary (x, pimag). The former are symmetric enclosing a finite area the latter are antisymmetric having null area. Nevertheless, the finite area accounts correctly for real discrete spectrum. We believe that with this, PT-symmetric quantum mechanics passes one of the most stringent tests towards a description that is consistent and compatible with conventional quantum mechanics.
Published Version
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