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Semiclassical Bohr quantization with a magnetic potential

  1. Aug 20, 2010 #1
    1. The problem statement, all variables and given/known data

    given the Hamiltonian in one dimension [tex] H= \frac{(p-eA)^{2}}{2m}+ V(x) [/tex]

    use the Bohr-Sommerfeld quantization in one dimension to obtain n=n(E)



    2. Relevant equations

    Hamiltonian , quantization



    3. The attempt at a solution

    from the usual quantization algorithm in one dimension i get

    [tex] \int_{0}^{a}dx (2m)^{1/2}(E-V(X))^{1/2}+ \int_{0}^{a}dxA(x) =nh[/tex]

    here 'a' is a turning point so V(a)=E , simply the contribution to n(E) by the magnetic potential is an integral of A(x)
     
  2. jcsd
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