The quantization of energy in the harmonic-oscillator potential: Power   series solution
  We write a computer program that uses the recursion relation to calculate wave function in the harmonic-oscillator potential for specified values of E/hv (with its deviation 0.001) containing only even numbers of v (0,2,4,...). In this work, differential equations are solved by power series methods, i.e. the Schrodinger equation stationary state wavefunction of the harmonic-oscillator. This technique is applied to obtain the wavefunction of the quantum harmonic oscillator and is at a more sophisticated level than elsewhere in the course of quantum physics. For the able student this can be a worthwhile extension to the work on the harmonic-oscillator. 
Omer Sise