Register to reply

Weak Form of the Effective Mass Schrodinger Equation

by Morberticus
Tags: effective, form, mass, schrodinger, weak
Share this thread:
Apr29-14, 04:09 PM
P: 81

I am numerically solving the 2D effective-mass Schrodinger equation

[itex]\nabla \cdot (\frac{-\hbar^2}{2} c \nabla \psi) + (U - \epsilon) \psi = 0[/itex]

where [itex]c[/itex] is the effective mass matrix

[itex]\left( \begin{array}{cc}
1/m^*_x & 1/m^*_{xy} \\
1/m^*_{yx} & 1/m^*_y \\
\end{array} \right)[/itex]

I know that, when the effective mass is isotropic, the weak form is
[itex]\int \frac{-\hbar^2}{2m^*}\nabla \psi \cdot \nabla v + U\psi vd\Omega = \int \epsilon \psi vd\Omega[/itex]

The matrix is giving me trouble however. Is this the correct form?

[itex]\int \frac{-\hbar^2}{2m^*_x}\frac{\partial u}{\partial x}\frac{ \partial v}{\partial x} + \frac{-\hbar^2}{2m^*_{xy}}\frac{\partial u}{\partial x}\frac{ \partial v}{\partial y} + \frac{-\hbar^2}{2m^*_{yx}}\frac{\partial u}{\partial y}\frac{ \partial v}{\partial x} + \frac{-\hbar^2}{2m^*_y}\frac{\partial u}{\partial y}\frac{ \partial v}{\partial y} + U\psi v d\Omega= \int \epsilon \psi v d\Omega[/itex]
Phys.Org News Partner Physics news on
Technique simplifies the creation of high-tech crystals
Working group explores the 'frustration' of spin glasses
New analysis of oxide glass structures could guide the forecasting of melt formation in planetary interiors
Greg Bernhardt
May6-14, 11:48 PM
Greg Bernhardt's Avatar
P: 9,336
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

Register to reply

Related Discussions
Form of Solution to Schrodinger Equation Quantum Physics 5
Proper form of schrodinger's equation? Quantum Physics 3
Summation Notation for Weak form of Differential Equation General Math 2
Weak form of Navier Stokes Equation Advanced Physics Homework 0
Schrodinger equation in matrix form Advanced Physics Homework 9