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Homework Help: Hamiltonian of charge in 2D

  1. Dec 1, 2014 #1
    1. The problem statement, all variables and given/known data
    charge e is within 2 dimensions in presence of magnetic field.

    H = 1/2m (p - e/c A)^2

    A = 1/2* B x r

    p and r have two components

    Show: H in terms of B along z axis resembles 2D HO (with some extra term)

    express H in terms of x, y, p_x, L_y

    2. Relevant equations

    L = r x p

    Hamiltonian for HO

    3. The attempt at a solution

    I plugged in B into H equation above so that gives:

    H = 1/2m [p- e/c (1/2*Bxr)]

    but i do not know what do do next. How do I express H in terms of B along z axis?
  2. jcsd
  3. Dec 1, 2014 #2


    User Avatar
    Gold Member

    Well, if you use the vector potential [itex] \vec A= B x \hat y [/itex], then you can find the complete calculation here. I'm not sure using other vector potentials, gives the same effect or not!
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