The spectrum of a one-dimensional Hamiltonian with potential V(x)=ix2 for negative x and \(V(x)=−ix^2\) for positive x is analyzed. The Schrodinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of an expression explicitly given in terms of Gamma functions. The spectrum consists of one real eigenvalue and an infinite set of pairs of complex conjugate eigenvalues.

http://arxiv.org/abs/1401.5937
Quantum Physics (quant-ph)