Quantum three-body system in D dimensions

Abstract

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schrödinger equation is reduced to the generalized radial equations satisfied by the generalized radial functions with a given total orbital angular momentum denoted by a Young diagram $[\mu ,\nu ,0,...,0]$ for the SO(D) group. Only three internal variables are involved in the functions and equations. The number of both the functions and the equations for the given angular momentum is finite and equal to $(\mu -\nu +1)$.

16 pages, no figure, RevTex, Accepted by J. Math. Phys

References in corpus (1)

• Independent Eigenstates of Angular Momentum in a Quantum N-body System

Cited by in corpus (8)

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• Three-body problem in $d$-dimensional space: ground state, (quasi)-exact-solvability
• The quantum n-body problem in dimension $d\ge n-1$: ground state
• Quantum four-body system in D dimensions
• Interdimensional degeneracies for a quantum three-body system in D dimensions
• Interdimensional degeneracies for a quantum $N$-body system in $D$ dimensions
• Helium-like ions in $d$-dimensions: analyticity and generalized ground state Majorana solutions
• 3-body harmonic molecule