A large class of bound-state solutions of the Schr\"odinger equation via Laplace transform of the confluent hypergeometric equation

It is shown that analytically soluble bound states of the Schr\"odinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric equation. It is also shown that all closed-form eigenfunctions are expressed in terms of generalized Laguerre polynomials. The generalized Morse potential is used as an illustration.