A criterion for the reality of the spectrum of PT symmetric Schroedinger operators with complex-valued periodic potentials

E. Caliceti, S. Graffi

Consider in $L^2(\mathbb{R})$ the \Sc operator family $H(g):=-d_x^2+V_g(x)$ depending on the real parameter $g$, where $V_g(x)$ is a complex-valued but $PT$ symmetric periodic potential. A…