Multichannel Dynamic Symmetry

J. Cseh
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J. Cseh: Institute of Nuclear Research of the Hungarian Academy of Sciences

A chapter in Symmetries in Science IX, 1997, pp 37-46 from Springer

Abstract: 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.

Keywords: Harmonic Oscillator; Shell Model; Cluster Model; Casimir Operator; Dynamic Symmetry (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-1-4615-5921-4_4

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