Quantum dynamics of a solvable nonlinear chiral model

Lakshmanan, M. ; Eswaran, K. (1975) Quantum dynamics of a solvable nonlinear chiral model Journal of Physics A: Mathematical & General, 8 (10). pp. 1658-1669. ISSN 1751-8121

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Official URL: http://iopscience.iop.org/0305-4470/8/10/018

Related URL: http://dx.doi.org/10.1088/0305-4470/8/10/018


The quantum mechanical analogue of a classical nonlinear system is shown to be exactly solvable and its energy levels and eigenfunctions are obtained completely. The symmetric version (k0=0) of this model is the SU(2)(X)SU(2) chiral invariant Lagrangian in the Gasiorowicz-Geffen coordinates. The radial part of the classical equation of motion (in both the symmetric and non-symmetric cases) admits simple harmonic bounded solutions and the bound state energies of the quantized system show a linear dependence on the coupling parameter lambda . It is shown that the Bohr-Sommerfeld quantization procedure reproduces the form of the correct bound state energy levels while a perturbation theoretic treatment gives the exact energy expressions. The ordering problem that arises in the quantum mechanical case is overcome.

Item Type:Article
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ID Code:19357
Deposited On:22 Nov 2010 12:44
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