Scale transformation method in self-consistent solution of Schrodinger andPoisson equations

A new scale transformation method is used in the solving of the Schrodinger equation. With this new method, the uniform grids used in the discretizati on in the conventional method are changed into nonuniform grids. Consequent ly, for some cases, the computing quantity is greatly reduced while maitain ing the required accuracy. The calculation of the quantized inversion layer in metal-oxide-semiconductor (MOS) structure is used to demonstrate the ef ficiency of the new method.