Unified treatment of a class of spherically symmetric potentials: quasi-exact solution (Q1681919)

Summary: We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of \(\mathrm{sl}(2)\). Then, we obtain the general exact solutions of the problem by employing the representation theory of \(\mathrm{sl}(2)\) Lie algebra.