The numerical method for one dimension quantum oscillator

In this paper we present a numerical method to solve the differential equation of a one-dimentional harmonic oscillator. This method is based on the expansion of the wave function over the orthogonal set. In this method the wave function and also the Hamiltonian of the oscillator is represented in a matrix form and the time-dependent Schrodinger equation is also rewriten in a matrix form. This matrix representation results in a set of linear equations. By solving these equations, the energy levels and the wave function of the oscillator can be estimated fairly. This method can be applied to solve the oscillators with perturbation.