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An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models

Valery P. Karassiov·Andrei B. Klimov
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Abstract

A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the $su_{pd}(2)$ shift operators and a (recursive) reduction of finding coefficient functions to solving auxiliary exactly solvable $su(2)$ problems with quadratic Hamiltonians. PACS numbers: 03.70; 02.20; 42.50

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Valery P. Karassiov, Andrei B. Klimov. 1994-04-19. An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models. https://doi.org/10.1016/0375-9601(94)90816-8

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