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Interaction between two excited hydrogen atoms

  1. Nov 15, 2011 #1
    hi all.

    i am trying to calculate the interaction between two excited hydrogen atoms, using degenerate perturbation theory. but comes up a few problems, any helps will be greatly appreciated.

    the perturbation has the form:

    H`=e3/R3(XaXb+YaYb-2ZaZb)
    where the R is the distancee between two atoms and a , b subscripts donates atom a and b respectively.

    i need to calculate the matrix elements have the form:
    (<ψaψb H` ψaψb>

    first thing is how to construct the total wave functions of the two atoms system? they add together or times together? and why? what is the physics meaning of:
    ψtotalaψb
    ψtotalab

    the second is, if using the exzact form, and ignor the radial funtion, is it possible to evaluate the matrix element? i.e
    for one atom in its 2 0 0 state and the other in its 2 1 0 state. then wavefunctions equal to theirs spherical harrmonics which are:

    2 0 0 state = 1/(2* square root pi )
    2 1 0 state = square root 3 /(2* square root pi) * cosθ

    couples to one atom in 2 1 0 state and the other in 2 1 1 state

    2 1 1 state = squre root (3)/2 * 1/(squre root (2* pi)) * sinθ*ei∅

    the first term yields:

    ∫∫∫2 0 0 state * Xa * 2 1 0 state dr sinθ dθ d∅ *∫∫∫2 1 0 state * Xb * 2 1 1 state dr sinθ dθ d∅

    since x= rsinθcos∅ and we have ignored the radial part, how can I evaluate dr ?
    above all, am I right for constructing the matrix element like the above way?

    Apologise for such a messy question, it is my first time to put equations up here, and I havent figured out how to construct a complex equation.

    Thank you in advance.
     
    Last edited: Nov 15, 2011
  2. jcsd
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