Factorization and q-deformed algebra of a quantum anharmonic oscillator

Abstract

We have studied the underlying algebraic structure of the anharmonic oscillator by using variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a supersymmetric form in terms of annihilation and creation operators which satisfy a q-deformed algebra. This algebraic structure is used to construct all the eigenstates of the Hamiltonian.