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

In this paper, we discuss the relation of thenonlinear Heisenberg algebras in two dimensions withlinear ones following the Nowicki and Tkachuk’s approachfor one-dimensional case. For one-dimensional harmonicoscillator, we obtain the solution explicitly. For the nonlinearHeisenberg algebras in two dimensions, we introducetwo generators to transform this algebra into the linearone. For the linear version of the nonlinear Heisenbergalgebras in two dimensions, we obtain the eigenfunctionfor the position and angular momentum operator and solvethe harmonic oscillator problem in two dimensions.