One-Dimensional Models

Abstract

One-dimensional models might appear in quantum mechanics in two, in a way, diametrically opposite situations. In one case, you can pretend that the potential energy of a particle changes only in one direction, such as a potential energy of a uniform electric field. Classically, this would mean a motion characterized by acceleration in one direction and constant velocity in perpendicular directions. By choosing an appropriate inertial coordinate system, you can always eliminate the constant velocity component and consider this motion as straightlinear. Quantum mechanically, this situation has to be described in the coordinate representation, and the respective coordinate wave function can be presented in the form