Interdimensional degeneracies for a quantum $N$-body system in $D$ dimensions

Abstract

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 $[\mu +n]$ in $(D-2n)$ dimensions are degenerate where $[\mu ]$ and $D$ are given and $n$ is an arbitrary integer if the representation $[\mu +n]$ exists for the SO($D-2n$) group and $D-2n\ge N$. 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.

arXiv comment8 pages, no figure, RevTex, Accepted by EuroPhys.Lett

References in corpus (4)

• Quantum three-body system in D dimensions
• Independent Eigenstates of Angular Momentum in a Quantum N-body System
• Quantum four-body system in D dimensions
• Interdimensional degeneracies for a quantum three-body system in D dimensions

Cited by in corpus (1)

• Inter-dimensional Degeneracies in van der Waals Clusters and Quantum Monte Carlo Computation of Rovibrational States