A modified Ricatti approach to partially solvable quantum Hamiltonians. I: Finite Laurent type potentials

Abstract

Partial solubility in quantum mechanics is investigated by studying the logarithmic derivative of the wave function. By explicitly isolating the singularities of the logaritmic derivative, a modified Ricatti equation for the regular component is obtained. For the finite Laurent series potentials considered, we derive the constraints on the coupling constants to obtain closed form solutions for a subset of eigenstates.