Connection between the hydrogen atom and the four-dimensional oscillator.

Abstract

The connection between the three-dimensional hydrogen atom and a four-dimensional harmonic oscillator (or equivalently a coupled pair of two-dimensional harmonic oscillators) subjected to a constraint condition is further explored. In particular, the role the constraint condition plays in determining the phase relationship between the pair of two-dimensional oscillators is examined. Furthermore, the connection is discussed in a group-theoretical context involving the Lie algebras of SO(4), SO(3,1), E(3), SO(4,2), and Sp(8,R).