Exponentially confining potential well

We introduce an exponentially confining potential well that can be used as a model to describe the structure of a strongly localized system. We obtain an approximate partial solution of the Schrödinger equation with this potential well where we find the lowest energy spectrum and the corresponding wavefunctions. We use the tridiagonal representation approach as the method for obtaining the solution as a finite series of square-integrable functions written in terms of Bessel polynomials.