2017/02/24 by C. R. Hägen, Hagen, C. R.
Physics and Astronomy · #FOS: Physical sciences #Laser-Matter Interactions and Applications #Mechanical and Optical Resonators #Photorefractive and Nonlinear Optics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1702.07659
openalex publication_date 2017/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.