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Carl R Hagen

Carl R Hagen

University of Rochester, USA

Title: Group theory, coherent states, and the N-dimensional oscillator


Biography: Carl R Hagen


The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1) x O(N) which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the one-dimensional oscillator are given for each value of the angular momentum parameter. This allows the construction of an infinite number of coherent states to be carried out. In the N=1 case there is a twofold family of coherent states, a particular linear combination of which coincides with the single set already well known for that case. Wave functions are readily derived which require only the solution of a first order differential equation, an attribute generally characteristic of group theoretical approaches.

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