Relation of the nonlinear Heisenberg algebras in two dimensions with linear ones

محورهای موضوعی : Journal of Theoretical and Applied Physics

Won Sang Chung ¹

1 - Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University

تاریخ پذیرش : 1394/06/10 تاریخ انتشار : 1394/06/10

کلید واژه: Nonlinear Heisenberg algebras, Algebra, Two dimensions,

چکیده مقاله :

AbstractIn this paper, we discuss the relation of the nonlinear Heisenberg algebras in two dimensions with linear ones following the Nowicki and Tkachuk’s approach for one-dimensional case. For one-dimensional harmonic oscillator, we obtain the solution explicitly. For the nonlinear Heisenberg algebras in two dimensions, we introduce two generators to transform this algebra into the linear one. For the linear version of the nonlinear Heisenberg algebras in two dimensions, we obtain the eigenfunction for the position and angular momentum operator and solve the harmonic oscillator problem in two dimensions.