On the quantum mechanics of complex Hamiltonian systems in one dimension

Abstract

The solutions of an analogous Schrödinger wave equation for the one-dimensional non-Hermitian Hamiltonian H(x, p) in the complex phase plane characterized by x = x1 + i p2, p = p1 + ix2, are investigated. The quasi-exact solutions thus obtained reveal a lot about the nature of the complex eigenvalue spectrum of the potential concerned. The examples of harmonic, harmonic plus inverse harmonic and Mörse potentials are discussed.