The bounded positive- and negative-parity spectrum E(?)n of the symmetric, one-dimensional, finite quantum square-well potential is computed exactly, explicitly and analytically in the form E(?)n = f(?)(n), where f(?) are known functions.
Abstract We present details of a new solution method for the bound energy states of a quantum particle in a one-dimensional symmetric finite square well potential. The solution is obtained in a clear way by introducing a simple method that relies on the use of two auxiliary functions. The approach is straightforward and leads to the well-known even and odd parity wave function solutions of the problem without having to do any a priori assumptions about the nature or symmetry of the quantum states.