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How to directly calculate the polarizability

  1. Apr 17, 2015 #1
    Dear all,
    I want to directly calculate the polarizability using the following perturbation expression,
    when the ground state wave function |0> is known.
    for example, for He atom, r1 and r2 two electrons.

    ##\alpha = \frac{2}{3}\left\langle {0|({r_1} + {r_2})\frac{1}{{H - {E_0}}}({r_1} + {r_2})|0} \right\rangle ##

    How to deal with the term of ## \frac{1}{{H - {E_0}}}## ?

    Any help or references will be appreciated.

    Best regards.
    Youzhao Lan
  2. jcsd
  3. Apr 17, 2015 #2


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    That's a bit a longer story. First, have a look on time-independent perturbation theory in a good textbook on quantum theory. The treatment in Sakurai is very good. Then look for the application on the Stark effect (2nd order perturbation theory).
  4. Apr 17, 2015 #3
    Thank you very much, I get it.

    Best regards.
  5. Apr 17, 2015 #4


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    Usually, you insert a resolution of the identity in terms of eigenfunctions of H, i.e. ## (H-E_0)^{-1}=\sum_i |i\rangle (E_i-E_0)^{-1}\langle i |##.
  6. Apr 27, 2015 #5
    Dear DrDu,
    Thank you very much! The infinite summation seems to be another difficult task for obtaining exact results.
    Best regards.
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