The Momentum Operator in The Infinite Square Well Problem of Quantum Mechanics

Abstract

The infinite square well (ISW) is usually the first problem involving bound states studied in quantum mechanics. Although it is straightforward to determine the stationary states and energy levels, the artificial structure of the problem leads to simple paradoxes involving quantization and measurability of momentum. We show how the boundary conditions influence the momentum operator , and discover the connections between momentum, differentiation and integration, which rescue the hermicity of  and its powers .