A COMPUTATIONAL FOURIER-SERIES SOLUTION OF THE BENDANIEL-DUKE HAMILTONIAN FOR ARBITRARY SHAPED QUANTUM-WELLS

A new technique for solving the BenDaniel-Duke Hamiltonian using a Fou rier series method is discussed. This method Fourier transforms the ef fective mass and potential profiles to calculate the eigenenergies and probability densities in transform space. Numerical solutions of the eigenenergies of a rectangular quantum well are compared to the finite difference, finite element, and tracer matrix methods. The eigenenerg ies of the envelope functions are computed and compared to the exact c ase made under a constant effective mass approximation for an asymmetr ic triangular and parabolic shaped quantum well. The necessity of usin g a variable effective mass in the BenDaniel-Duke Hamiltonian is shown by a comparison of the eigenenergies in the constant and variable eff ective mass cases. The Fourier series method is then used to analyze t he effects of compositional gradients and electric fields on the eigen energies and envelope functions for asymmetric coupled asymmetric tria ngular quantum wells.