The model of q -deformed ∑-type three-le v el atom was constructed by means of the reationship between hydrogen atom and 4- dimensional harmonic oscillator.It was worked out that the energy levels of q -deformed ∑-type atom were split.
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.