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Dynamics and spectral properties of a quantum 2D bounded vortex system

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  • Penna, Vittorio

Abstract

A system of two 2D, interacting vortices in the presence of straight reflecting walls is considered. Both the cases of a vortex-vortex pair and of a vortex-antivortex pair are studied. The system Hamiltonian includes the strongly non-linear contribution due to the vortex-boundary interaction. We analyze first the classical vortex motion then, resorting to the canonical quantization procedure, we find the quantum spectra. The quantization conditions result in the appearance of a denumerable class of constraints for the prime integrals. Further we discuss a complete solution of the wave equations showing that it leads to an extension of the class of known spheroidal eigenfunctions.

Suggested Citation

  • Penna, Vittorio, 1988. "Dynamics and spectral properties of a quantum 2D bounded vortex system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(3), pages 400-419.
    • Handle: RePEc:eee:phsmap:v:152:y:1988:i:3:p:400-419
    DOI: 10.1016/0378-4371(88)90196-3
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