Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Boundary conditions for two dimensional problems in Quantum mechanics

  1. Oct 25, 2009 #1
    I am stuck at the problems of Boundary conditions for two dimensional problem in QM.
    iIf we have a two-dimensional domain,
    along the boundary, we can define two directions, one is tangential, the other is normal,
    assuming that there is no current flowing in and out along the normal direction.
    How can we define the boundary conditions?
    To be specific, we have the following wavefunction in the domain
    [tex]\psi({\vec r})=e^{i{\vec k}_i\cdot {\vec r}}+r e^{-i{\vec k}_f\cdot {\vec r}}[/tex]
    while outside the domain, we have
    [tex]\psi({\vec r})=e^{i{K}_s S-K_n N}[/tex]
    [tex]K_s, K_n[/tex] is the tangential and normal components of the momentum [tex]{\vec K}[/tex] outside the domain.
    S,N are the coordinates of the position vector [tex]{\vec R}[/tex]
     
    Last edited: Oct 25, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Boundary conditions for two dimensional problems in Quantum mechanics
Loading...