Quantum four-body system in D dimensions

Abstract

By the method of generalized spherical harmonic polynomials, the Schrödinger equation for a four-body system in $D$-dimensional space is reduced to the generalized radial equations where only six internal variables are involved. The problem on separating the rotational degrees of freedom from the internal ones for a quantum $N$-body system in $D$ dimensions is generally discussed.

arXiv comment19 pages, no figure, RevTex, Submitted to J. Math. Phys

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• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Benchmark Test Calculation of a Four-Nucleon Bound State
• Casimir effect for a $D$-dimensional sphere
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• Quantum three-body system in D dimensions
• Independent Eigenstates of Angular Momentum in a Quantum N-body System
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• Stability of three-and four-charge systems

Cited by in corpus (7)

• Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions
• Solvable few-body quantum problems
• Four-body (an)harmonic oscillator in $d$-dimensional space: $S$-states, (quasi)-exact-solvability, hidden algebra $sl(7)$
• Four-body problem in d-dimensional space: ground state, (quasi)-exact-solvability. IV
• Interdimensional degeneracies for a quantum $N$-body system in $D$ dimensions
• Exactly solvable $N$-body quantum systems with $N=3^k(k\ge 2)$ in the $D=1$ dimensional space
• On the four-body problem in the Born-Oppenheimer approximation