Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dipole approximation in acceleration form

  1. Sep 22, 2011 #1

    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


    User Avatar
    Homework Helper

    first work out the commutators:




    and so on...

    Then expand V as a power series and use the above commutators to prove the relation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook