Factorization and q-deformed algebra of a quantum anharmonic oscillator

We have studied the underlying algebraic structure of the anharmonic oscill ator by using variational perturbation theory. To the first order of the va riational perturbation, the Hamiltonian is found to be factorized into a su persymmetric form in terms of annihilation and creation operators which sat isfy a q-deformed algebra. This algebraic structure is used to construct al l the eigenstates of the Hamiltonian.