Abstract-The paper presents the faster, simpler, and accurate algorithm to solve time independent Schrödinger equation based on transfer matrix method. We can thus calculate all bound and quasi bound energy and the corresponding probability density. A central part of this paper deals with the solving of Schrödinger equation for quantum well structure. Our results show that the transfer matrix method is accurate, it is easier to implement. The increase in well width increases the FWHM from 5.4 nanometer to 9.4 nanometer, while the increase in the Aluminum concentration the FWHM decreases from 8.98 to 5.4.