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

Carl M Bender, Daniel W Hook, Lawrence R Mead

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…