Europhys. Lett., 64 (5) , pp. 586-591 (2003)
Interdimensional degeneracies for a quantum N-body system in D dimensionsXiao-Yan Gu1, 2, Zhong-Qi Ma1, 2 and Jian-Qiang Sun2
1 CCAST (World Laboratory) - P.O. Box 8730, Beijing 100080, PRC
2 Institute of High Energy Physics - Beijing 100039, PRC
(Received 28 April 2003; accepted in final form 16 September 2003)
The complete spectrum of exact interdimensional degeneracies for a quantum N-body system in D-dimensions is presented by the method of generalized spherical harmonic polynomials. In an N-body system all the states with angular momentum in (D-2n) dimensions are degenerate where and D are given and n is an arbitrary integer if the representation exists for the SO(D-2n) group and . There is an exceptional interdimensional degeneracy for an N-body system between the state with zero angular momentum in D=N-1 dimensions and the state with zero angular momentum in D=N+1 dimensions.
03.65.-w - Quantum mechanics.
03.65.Ge - Solutions of wave equations: bound states.
03.65.Fd - Algebraic methods.
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