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Raising and lowering operators

  1. Jun 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Can anyone please explain why any term which is a product of 4 raising and lowering operators with a lowering operator on the extreme right (eg. A-A+A+A-) has zero expectation value in the ground state of a harmonic oscillator?



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 14, 2009 #2

    Cyosis

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    What happens if you let the lowering operator work on [itex]\psi_1[/itex]? What do you get when you let the lowering operator work on [itex]\psi_0[/itex]?

    Calculate [itex]a \psi_1[/itex] and [itex]a \psi_0[/itex]. Does [itex]a \psi_0[/itex] exist?
     
  4. Jun 14, 2009 #3
    I get it now... thank you. When the lowering operator operates on v1, I get v0. When it operates on v0, I get zero. A- v0 doesn't exist so the rest of the operators in the product have nothing to operate on.

    Cheers.
     
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