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Normalizaed wave function of the hydrogen atom

  1. Dec 5, 2005 #1
    how do you find the normalized wave functions of the hydrogen atom for n=1, l=0 and ml=0?
    in my textbook, it's a table, but i have no idea where the figures come from...
     
  2. jcsd
  3. Dec 5, 2005 #2

    jtbell

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    Staff: Mentor

    You do it by finding the solution for the Schrödinger equation for the hydrogen atom. This means finding the solutions of the individual differential equations for the functions [itex]R(r)[/itex], [itex]\Theta(\theta)[/itex] and [itex]\Phi(\phi)[/itex].

    Many introductory textbooks work through the solution for [itex]\Phi(\phi)[/itex] because its equation is rather easy. But I didn't see the complete solution for [itex]\Theta(\theta)[/itex] and [itex]\Phi(\phi)[/itex] until my graduate school QM courses. They're that messy! :yuck:

    Oh wait, I was thinking of the general solution for any n, l, m. You want specifically n=1, l=0, m=0. That case might not be too bad, after you substiute those values of n, l, m into the individual differential equations for the three variables. [itex]\Theta(\theta)[/itex] and [itex]\Phi(\phi)[/itex] both turn out to be constant in this case, so their differential equations must be very simple! :smile:
     
    Last edited: Dec 5, 2005
  4. Dec 5, 2005 #3
    [itex]\Theta(\theta)[/itex]
    but the original function isn't known, right? so how do you solve it?
     
  5. Dec 5, 2005 #4

    jtbell

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    Staff: Mentor

    That's what the Schrödinger equation is for, or rather the individual ordinary differential equations that you get after you separate the S.E.

    Solving an algebraic equation like [itex]x^2 - 5x + 6 = 0[/itex] gives you a number for [itex]x[/itex], or a set of numbers. Solving a differential equation like [itex]d^2 \Phi(\phi) / d \phi^2 = -m_l^2 \Phi(\phi)[/itex] gives you a function for [itex]\Phi(\phi)[/itex], or a set of functions.
     
  6. Dec 6, 2005 #5
    thank you very much!!! :)
     
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