PT-symmetric momentum operator and bound states

Abstract

We develop further the concept of generalized extended momentum operator, which has been proposed very recently in (Izadparast and Mazharimousavi 2020Phys. Scr.95, 075220). In particular, we introduce a PT-symmetric generalized momentum operator using a complex auxiliary function. The resulting Hamiltonian constructed based on the newly proposed momentum is not Hermitian, however, provided a proper potential it may be pseudo-Hermitian with corresponding real energy eigenvalues. An explicit example is presented to verify the application of the suggested non-Hermitian momentum.