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Sudden Perturbation Approximation Question

  1. May 13, 2008 #1
    1. The problem statement, all variables and given/known data
    In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+


    2. Relevant equations
    |<n'l'm'|nlm>|^2


    3. The attempt at a solution

    I actually know the answer to this but I am not clear as to why and I am wondering if there is an easier way to determine the solution.

    The answer comes out to be 0. When integrating the wavefunctions |n'l'm'> and |nlm> in spherical coordinates to calculate the inner product (i.e. the probability amplitude), the integral over [tex] d\theta[/tex] returns 0. Is there an easier way to see this other than going through the calculations?

    How is this result interpreted?

    Thanks,

    jsc
     
  2. jcsd
  3. May 13, 2008 #2

    nrqed

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    The spherical harmonics are orthonormal so <l' m' | l m> is zero unless l=l' and m= m'. Clearly here the result is zero since |3,0> is orthogonal to |0,0>

    Physically, it simply says that a particle in an s state has no angular momentum so the probability of it being observed with l=3 is zero. The sudden approximation simply assumes that the transition was so quick that the orbital angular momentum of the electron remained unchanged.
     
    Last edited: May 13, 2008
  4. May 13, 2008 #3
    Thanks nrged.

    That makes it clear.
     
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