1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    dbd8f853d8d1e754b5089385733a4f9a.png

    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

    ShayanJ

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Hamiltonian of charge in 2D
  1. The Hamiltonian (Replies: 9)

  2. Hamiltonian Question (Replies: 1)

Loading...