Analytic approximation for eigenvalues of a class of PT -symmetric Hamiltonians

Abstract

An analytical approximation for the eigenvalues of PT-symmetric Hamiltonian H=-d2/dx2-(ix)ϵ+2, ϵ>-1 is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of ϵ>-1.