Quantum Mechanics => Operators

  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?

    thanks
     
  2. jcsd
  3. ahrkron

    ahrkron 734
    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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