Solving Schrodinger Equation with Non-Uniform Grids by Scale Transformation Method

A new scale transformation method is used in solving the Schrodinger equation. With it, the uniform grids in the discretization in conventional method are changed into non-uniform grids. Consequently, in some cases, the computing quantity will be greatly reduced at keeping the required accuracy. The calculation of the quantized inversion layer in MOS structure is used to demonstrate the efficiency of the new method.