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QM: commutator 2D particle magnetic field

  1. Nov 1, 2015 #1
    1. The problem statement, all variables and given/known data
    I was reading this textbook:
    https://books.google.com/books?id=s...10#v=onepage&q=orbit center operators&f=false

    2. Relevant equations
    In the equation of the page (unlabeled), we have
    $$
    \left[A_x\frac{\partial}{\partial y} - \frac{\partial}{\partial y}A_x + \frac{\partial}{\partial x}A_y - A_y\frac{\partial}{\partial x}\right]\psi(x)\\
    = \left[- \frac{\partial A_x}{\partial y}+ \frac{\partial A_y}{\partial x}\right]\psi(x)
    $$

    3. The attempt at a solution
    Why do the first and fourth terms cancel out? Is it to do with the circular motion of the charged particle in the magnetic field?
     
  2. jcsd
  3. Nov 1, 2015 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    For example, for the second term in the first line of your equation
    $$
    - \frac{\partial}{\partial y}(A_x \psi(x)) = - A_x \frac{\partial \psi(x)}{\partial y} - \psi(x)\frac{\partial A_x}{\partial y}
    $$
    The first term of the right hand side in the above equation will cancel with the first term in
     
  4. Nov 1, 2015 #3
    Oh. That makes it clear. Thank you.
     
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