Solution of the 1d Schrödinger Equation for a Symmetric Well

Abstract

We suggest a mathematical potential well with spherical symmetry and apply to the 1d Schrödinger equation. We use some well-known techniques as Stationary Perturbation Theory and WKB to gain insight into the solutions and compare them to each other. Finally, we solve the 1d Schrödinger equation using a numerical approach with the so-called Numerov technique for comparison. It can be a good exercise for undergrad students to grasp the above-cited techniques in a quantum mechanics course.

8 pages, 7 figures

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