$sl(2)$ variational schemes for solving one class of quantum nonlinear models

Details $sl(2)$ variational schemes for solving one class of quantum nonlinear models $sl(2)$ variational schemes for solving one class of quantum nonlinear models

1996-08-12

arxiv.org/abs/quant-ph/9608016v1

Physics

Quantum Physics

9 pages, LATEX

Scientific paper

Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational schemes, based on $sl(2)$ generalized coherent states as trial functions, for solving both spectral and evolution tasks. In such a manner a new analytical expression is found for energy spectra in a mean-field approximation which is beyond quasi-equidistant ones obtained earlier.

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