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Journal of Yiyang Teachers College

The Relationship between the Two-dimensivnal Hydrogen Atom and the Two-dimensional Harmonic oscillator

Yang Liu

Published Jan 1, 2001• 0 citations
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Abstract

In this paper,We work out the relationship between the energy eigenfunction,the energy eigenvalues of the two-dimensional hydrogen atom and those of the two-dimensional harmonic oscillator in terms of su(1,1) algebra.The their coordinate trans formation is worked out.

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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).