An su(1,1) algebraic method for the hydrogen atom

Abstract

An algebraic solution for the hydrogen atom analogous to the one recently proposed to solve the relativistic version of the system is presented. We add to the usual radial description of the problem an additional angular variable and an associated operator which can be considered as part of an su(1, 1) Lie algebra. The operators of the algebra define radial ladder operator relating the eigenfunctions of the system in unit steps of the principal quantum number. We conclude that the radial bound states of the hydrogen atom in our extended configuration space can be regarded as spanning the minimal M representation of the su(1, 1) Lie algebra. The method can also be extended to solve the s-wave Morse problem and the three-dimensional harmonic oscillator.