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Quadratic Stark Effect - Perturbation Theory

  1. Apr 6, 2014 #1
    1. The problem statement, all variables and given/known data

    2u9nwk0.png

    2. Relevant equations



    3. The attempt at a solution

    With a parity operator, Px = -x implies x has odd parity while Px = x implies x has even parity.

    Things that puzzle me

    1. Why is ##[H_0,P] = 0## and ##H_1P = -PH_1##? Is it because ##H_1 \propto z## so ##Pz = -z##? Then shouldn't it be ##PH_1 = -H_1##?

    2. For any operator R, it is represented by a matrix ##R_{ij} = <i|R|j>##. In this case is the operator in question ##PH_1 + H_1P##? What does 'matrix element between two parity states' mean? From what I see, ##<n'l'm'p'|PH_1 + H_1P|nlmp>## is simply the addition of two matrices, one corresponding to ##PH_1## and another ##H_1P##. Which has odd/even parity and why?

    3. Why do all diagonal matrix elements vanish?
     
  2. jcsd
  3. Apr 8, 2014 #2
  4. Apr 12, 2014 #3
    bumpp
     
  5. Apr 14, 2014 #4
  6. Apr 18, 2014 #5
    bumpp
     
  7. Apr 21, 2014 #6
    Would appreciate clarifying doubts on the 3 points above!
     
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