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arXiv · 1312.5104

Relation of deformed nonlinear algebras with linear ones

A. Nowicki·V. M. Tkachuk
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Abstract

The relation between nonlinear algebras and linear ones is established. For one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated on the example of harmonic oscillator.

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A. Nowicki, V. M. Tkachuk. 2013-12-18. Relation of deformed nonlinear algebras with linear ones. https://doi.org/10.1088/1751-8113%2F47%2F2%2F025207

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