An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models
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 supd(2) as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the supd(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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