Quantum mechanics of $PT$ and non-$PT$ -symmetric potentials in three dimensions

摘要

With a view of exploring new vistas with regard to the nature of complex eigenspectra of a non-Hermitian Hamiltonian, the quasi-exact solutions of the Schr??dinger equation are investigated for a shifted harmonic potential under the framework of extended complex phase-space approach. Analyticity property ofthe eigenfunction alone is found sufficient to throw light on the nature of the eigenvalues and eigenfunctions of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as excited state including their $PT$-symmetric version are worked out.