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Harmonic Oscillator Operators?

  1. Oct 19, 2006 #1
    I worked these problems out:

    [x, H] = xH - Hx = 0

    [p, H] = pH - Hp = non-zero

    H is the harmonic oscillator Hamilitonian, x and p are the position and momentum operators, respectively.

    My question is, why doesn't p commute with H, but x does???
  2. jcsd
  3. Oct 19, 2006 #2
    If you worked out these explicitly this should be pretty clear. The potential term commutes with x but not with p.
  4. Oct 20, 2006 #3

    Meir Achuz

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    I don't think [H,x]=0.
  5. Oct 23, 2006 #4


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    The commutator of X with the KE, p*p/2m, is not zero; the commutator is proportional to p, the momentum.
    Reilly Atkinson

    Harmonic oscillator commutators are discussed in almost any QM text,
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