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Die Klassifikation nach inneren Symmetrien beim quantenmechanischen Mehrkörperproblem

I. Allgemeine Behandlung des Mehrkörperproblems in reduzierten Koordinaten

Classification according to internal symmetries in the quantum-mechanical many-body-problem

I. General analysis of the many-body-problem in reduced coordinates

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Zeitschrift für Physik

Abstract

On introducing relative and centre-of-mass coordinates, the HamiltonianH of a system ofn identical particles with two-body interaction separates into a centre-of-mass Hamiltonian and a centre-of-mass-independent HamiltonianH i formally describing a system ofn-1 “reduced” particles. The objective of this paper is firstly to investigate the connection between the symmetries of the actual and the reduced system and secondly to discuss the consequences of symmetries ofH i on the classification and construction of the eigenstates ofH. Angular momentum and parity properties are found to be coincident in the actual and the reduced system. Group-theoretical considerations lead to a method for the determination of reduced vectors with simple transformation properties under permutations of the position vectors which define the reduced vectors. The method is used to construct “optimal” reduced vectors for the three- and four-body-problem. It is proved that similar “optimal” reduced vectors do not exist forn>4.

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Authors and Affiliations

  1. Institut für Theoretische Physik der Universität Erlangen-Nürnberg, Deutschland

    G. Wunner, H. Ruder & H. Volz

Authors
  1. G. Wunner
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  2. H. Ruder
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  3. H. Volz
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Wunner, G., Ruder, H. & Volz, H. Die Klassifikation nach inneren Symmetrien beim quantenmechanischen Mehrkörperproblem. Z. Physik 267, 305–312 (1974). https://doi.org/10.1007/BF01669453

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  • DOI: https://doi.org/10.1007/BF01669453

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