One dimensional harmonic oscillator's energy eigenvalue is solved by the ways o f matrix dynamics way,raising and lowering operator way,coherent state way and double wave function way.Several simple ways of solving harmonic oscillator's en ergy level are given.
By means of quadratic theory,we present a general method to solve the energy eigenvalue of coordinate and momentum coupling of n-dimensional harmonic oscillator.To apply this method to solve the energy eigenvalue of two-dimensional and three-dimensional coupling harmonic oscillator,our conclusion is the same with the others.Since the present method does not require a specific form of transformation matrix,this makes it be simple to solve the eigenvalue of a symmetrical form Hamilton and easy to calculate the results.This method is a universal and very effective algebraic method.
Linear harmonic oscillator takes an important role in quantum mechanics.Many systems can be taken approximately as of linear harmonic oscillator.Consequently,the study on linear harmonic oscillator is significant in many ways.Using methods of formula and perturbation,this paper finds out the energy eigenvalue of one-dimensional linear harmonic oscillator in weak electric field,and presents clearly two typical solutions for the energy level of one-dimensional linear harmonic oscillator in weak electric field.