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S.E. Hydrogen

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the values of l and a for which the function R(r) = Cexp[-r/a], where C and a are constants, is a solution of the radial equation for the hydrogen atom.

    Then find the energy in terms of the rydberg constant and the magnitude of the angular momentum. Finally state the spectrospic name (eg 1s) of the electron.

    2. Relevant equations



    3. The attempt at a solution

    So I substituted R(r) = u(r)/r and got to here (see attached). I assume I'm supposed to compare coefficients but this leaves me with the columb term floating there. Any hints?

    [
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Oct 25, 2007 #2

    nrqed

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    I am confused. You say R = c e(-r/a) here but in your attachment you use r e^(-r/a).

    In addition, in your attachment, if we use the R given there, u(r) should be r^2 e^(-r/a)

    :confused:
     
    Last edited: Oct 25, 2007
  4. Oct 25, 2007 #3
    Oops yeah, messed up at the start. I'll have another go and report back.
     
  5. Oct 25, 2007 #4

    nrqed

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    I am sure it will work now.
     
  6. Oct 25, 2007 #5
    This looks better.
     

    Attached Files:

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