A Noninvariance Group for the N-Dimensional Isotropic Harmonic Oscillator
19776 pages
Published in:
- J.Math.Phys. 18 (1977) 1952-1957
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Abstract: (AIP)
A semidirect product of the Weyl group N, with the special unitary groupSU(n), is proved to be a possible noninvariance group for the n‐dimensional isotropic harmonic oscillator. In order to obtain this result, a method is developed for finding the representation W of SU(n) which intertwines the representations U N v and (A+i B) U N v of N [where A+i BεSU(n)]; it is also shown that W=⊕∞ a=0 W a , where W a is an irreducible representation of SU(n), of dimension equal to the degeneracy of the (a+1)th energy level of the n‐dimensional isotropic harmonic oscillator.- GROUP THEORY
- SYMMETRY: SU(N)
- QUANTUM MECHANICS
- MODEL: OSCILLATOR
- ALGEBRA: WEYL
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