Solving for three-dimensional central potentials using matrix mechanics. (arXiv:1211.5236v1 [physics.class-ph])

Solving for three-dimensional central potentials using matrix mechanics. (arXiv:1211.5236v1 [physics.class-ph]):
Matrix mechanics is an important component of an undergraduate education in
quantum mechanics. Unfortunately it is generally taught only in the abstract,
with real implementations relegated to more advanced degrees, and usually in
the context of many-body physics. In this paper we present several examples of
the use of matrix mechanics to solve for a number of three dimensional problems
involving central forces. These include examples with which the student is
familiar, such as the Coulomb interaction -- in this case we obtain excellent
agreement with exact analytical methods, -- along with other interesting
`non-solvable' examples, such as the Yukawa potential. Much less mathematical
expertise is required for these methods, while some minimal familiarity with
the usage of numerical diagonalization software is necessary.