On approximating the free harmonic oscillator by a particle in a box
  The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box wavefunctions as trial wavefunctions, with the size of the box as the variation parameter, approximate eigenenergies and the corresponding eigenfunctions are obtained for the one dimensional free harmonic oscillator. 
Kunle Adegoke, Adenike Olatinwo, Henry Otobrise, Rauf Giwa and Gbenga   Olunloyo
quant-ph