Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra

The spectrum of the Hermitian Hamiltonian H=p^2+V(x) is real and discrete if the potential V(x)\to\infty as x\to\pm\infty. However, if V(x) is complex and PT-symmetric, it is conjectured that, except in rare special cases, V(x) must be analytic in order to have a real spectrum. This conjecture is demonstrated by using... Show more