  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.
