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 $s{u}_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the $s{u}_{pd}(2)$ 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

(11pages). LATEX

References in corpus (1)

• Higher-Derivative Supersymmetry and the Witten Index

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