Generalized deformed oscillator and nonlinear algebras

Abstract

The harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied. The eigenstates and eigenvalues of the deformed oscillator are calculated. This generalized deformed oscillator algebra is used to create nonlinear deformation of the classical SU(2) algebra. The deformed boson realizations of an arbitrary nonlinear SU(2) algebra are calculated. The algebra of the q-deformed oscillator is a special case of the generalized deformed oscillator algebra.