Abstract
An algebraic approach to solving a class of one-particle Schrödinger equations is presented. As an example, quasi-exact solutions of the eigenvalue problem of a Hamiltonian describing two interacting particles confined in a parabolic well are obtained. This example constitutes a unification and a generalization of several models known in the literature, as the ones of Taut (Phys. Rev. A 1993, 48, 3561) and of Samanta and Ghosh (Phys. Rev. A 1990, 42, 1178). Two confined particles interacting by Coulomb forces and the nuclear motion of a diatomic molecule are discussed as practical implementations.
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