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Multichannel Dynamic Symmetry

In: Symmetries in Science IX

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  • J. Cseh

    (Institute of Nuclear Research of the Hungarian Academy of Sciences)

Abstract

A quantum mechanical system is said to have a continuous symmetry desrcibed by a Lie group G, if its Hamiltonian commutes with all the generators of the group, i.e. it can depend on the generators only through the Casimir invariants of the group. If both the potential and the total energy is invariant, the symmetry is called geometric, contrary to the dynamic symmetry which leaves invariant only the total energy [1]. Well-known examples are the O(4) dynamic symmetry of the Coulomb problem, and the U(3) dynamic symmetry of the harmonic oscillator problem. In both cases O(3) is a geometric symmetry. These kind of exact dynamic symmetries hold only for very special forces, therefore in this strict form they are not very helpful in building up models of few and many-body systems.

Suggested Citation

  • J. Cseh, 1997. "Multichannel Dynamic Symmetry," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science IX, pages 37-46, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-5921-4_4
    DOI: 10.1007/978-1-4615-5921-4_4
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