Collect. Czech. Chem. Commun. 2005, 70, 864-880

A Class of Exactly Solvable Schrödinger Equations

Jacek Karwowski* and Lech Cyrnek

Instytut Fizyki, Uniwersytet Mikołaja Kopernika, Grudziądzka 5, 87-100 Toruń, Poland


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.

Keywords: Schrödinger equation; Quasi-exactly solvable models; Harmonium; Confined quantum systems; Hamiltonian; Coulombic forces; Exponential ansatz; Quantum chemistry.

References: 16 live references.