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Dipole approximation in acceleration form

  1. Sep 22, 2011 #1
    hi,

    I have 2 localized states in a hydrogenic atom.. we're in dipole approimation.
    I have to proof that

    <b| [p,V] | a> = <b| grad(V) |a>
    or equally:
    <b| V grad |a> = 0

    (this is the dipole approximation in acceleration form)

    someone can help me?

    you can see http://books.google.it/books?id=1oXrE5YV19IC&pg=PA321&lpg=PA321&dq=dipole+approximation+matrix&source=bl&ots=cEbdhO2-ne&sig=pHxoDCxTrGi6ySPBRAF9tsws4Vc&hl=it&ei=fAd7TtH5GoLP0QXj48SjAw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB4Q6AEwADgK#v=onepage&q&f=true" [Broken]

    page 323 eq (8.22)

    thanks :)
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 23, 2011 #2

    olgranpappy

    User Avatar
    Homework Helper

    first work out the commutators:

    [p,x]=?

    [p,x^2]=?

    [p,x^3]=?

    and so on...

    Then expand V as a power series and use the above commutators to prove the relation.
     
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