Step Momentum Operator

Abstract

In the present study, the concept of a quantum particle with step momentum is introduced. The energy eigenvalues and eigenfunctions of such particles are obtained in the context of the generalized momentum operator, proposed recently in [13, 14]. While, the number of bound states with real energy for the particles with Hermitian step momentum inside a square well is infinite, it is finite for a particle with \mathcal{PT} -symmetric momentum.

14 pages, 4 figures and 2 tables