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It is shown that analytically soluble bound states of the Schr\"odingerequation for a large class of systems relevant to atomic and molecular physicscan be obtained by means of the Laplace transform of the confluenthypergeometric equation. It is also shown that all closed-form eigenfunctionsare expressed in terms of generalized Laguerre polynomials. The generalizedMorse potential is used as an illustration.

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