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

Hamiltonian matrix for two electrons in a 1D infinite well

  1. Jan 25, 2016 #1
    Hi everyone,
    I need help for preparing a Hamiltonian matrix.

    What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well):

    [itex]-\frac{ħ^{2}}{2m}[/itex][itex](\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) + \frac{q}{4πε_0ε_r(x_1-x_2)}ψ(x_1,x_2)=Eψ(x_1,x_2)[/itex]

    Any advice or suggestion would be really helpful for me.

    [probably the problem is an intermediate level problem. I mistakenly selected advance level. And, now I can't edit it]

    Thank you very much in advance......
    :)
     
    Last edited: Jan 25, 2016
  2. jcsd
  3. Jan 25, 2016 #2
    The matrix elements depend on the choice of basis.

    A reasonable choice of basis might be the solution of a single electron in the infinite well, that is considering the infinite well with one electron as the unperturbed problem and the second electron as the addition.

    However, perturbation theory doesn't work well when the additional term in the Hamiltonian (the perturbation) can be comparable to or larger than the original terms.

    This forum has discussed similar problems before:

    https://www.physicsforums.com/threa...f-two-electrons-in-a-1-d-infinite-well.15277/
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hamiltonian matrix for two electrons in a 1D infinite well
Loading...