Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials

Marcin Piatek, Artur R. Pietrykowski

The Schroedinger eigenvalue problems for the Whittaker-Hill potential $Q_2(x)=\frac{1}{2}{h}^2\cos 4x+4h\mu \cos 2x$ and the periodic complex potential $Q_{1}(x)=\tfrac{1}{4}h^2{\rm e…