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Quantum Mechanics => Operators

  1. May 22, 2003 #1
    I'm doing some past papers for my QM finals and I've come across a question that is a bit strange. I'm not sure if it's as easy as it sounds.

    X and P are one dimensional position and momentum operators, which take the explicit forms of x and -ihd/dx.

    i) write down the explicit forms of X^2 and P^2

    now then, is this just x^2 and hd^2/dx^2?

    im ok on the next few bits, but:

    iv) which, if any, of the two functions exp(ikx) and exp(-ax^2) are eigenfunctions of P^2?

    my guess is that, since the eigenfunction of P is exp(ikx), its the other one (and the i has disapeared in the squaring process), but how can i prove this?

    Im probably just being paranoid, but can someone verify these answers?

  2. jcsd
  3. May 22, 2003 #2


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    Staff Emeritus
    Gold Member

    How did you obtain them? that's the important part. I think you're missing a sign on P^2.

    Remember what an eigenfunction is. You need to plug in both functions on P^2, and see if you get a constant times the original function.
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