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

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

1994-04-06

arxiv.org/abs/hep-th/9404027v2

Physics

High Energy Physics

High Energy Physics - Theory

(11pages). LATEX

Scientific paper

10.1016/0375-9601(94)90816-8

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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