NOVEL NUMERICAL METHOD FOR THE SOLUTION OF SCHRÖDINGER'S EQUATION: EXCITON ENERGY OF CdS QUANTUM DOTS

Studying the quantum size effects on the exciton energy of two-dimensional CdS quantum dots in the single band effective mass approximation for both electron and hole, we use a finite confinement in the x–y plane and we assume also that the induced charge is spread along a very thin interface in the z-direction. Solving the Schrödinger equation with a new numerical method, which is called potential morphing method, we obtain the corresponding energy within the self-consistent Hartree scheme. Excellent agreement is obtained with the experimental values of exciton energies for various sizes of CdS quantum dots in the strong, medium and weak confinement limit.