Concerning Of Smoothed Wave Functions Instead Of Discontinuous Wave Functions In Quantum Mechanics

In this paper we investigate the discontinuity of the wave function in non-relativistic quantum mechanics. When due to discontinuity points the initial wave function of the system cannot be put to the Schrödinger equation & in some cases it is almost impossible to solve, then we define a smoothed wave function which is a limit state of the initial wave function. This can be embedded into the Schrödinger equation and the appropriate potential is obtained accordingly. It seems, in a famous instance of particle in a box, discontinuity of the wave function at one point has no trouble and one can put it into the Schrödinger equation. However, when facing with at least two points, we inevitably use another method.