Confluent hypergeometric equations and related solvable potentials in quantum mechanics

The connection between the Schrodinger and confluent hypergeometric equatio ns is discussed. It is shown that the factorization of the confluent hyperg eometric equation gives a unifying powerful algebraic tool in order to stud y some quantum mechanical eigenvalue problems. That description includes th e linear and N-dimensional harmonic oscillators, as well as the Coulomb and Morse potentials. (C) 2000 American Institute of Physics. [S0022-2488(00)0 2912-1].