Wavelet Method in Numerical Modeling of Quantum Dots Embedded in Matrix

Abstract

An analytical method of the solution of the governing nonlinear eigenproblem is proposed. It can be directly applied into the analysis of eigenstates in quantum mechanics. The method is based on the use of the separation of variables for specific shapes of quantum dots. In this way the analysis can be reduced to the disretization along one variable only the Daubechies wavelets. The eigenstates are derived with the use of the variational formulation combined with the method of the Rayleigh quotient