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Quick QM question(s)

  1. Oct 9, 2012 #1
    I'm trying to "sure"up my Quantum Mechanics and found an sheet of mostly conceptual review questions. A sort of "Quantum minima".

    I'd like to check my answers to a couple of these.

    Firstly:

    In terms of state vector the wavefunction is the expansion coefficient (probability amplitude) of a state i.e

    [tex] \psi = \langle x \left | \psi \right\rangle [/tex]

    What happens if you put an operator (e.g. p) between the bra and ket as if you were calculating an expectation value? i.e.

    [tex] \left\langle x \left | p \right | \psi \right \rangle [/tex]

    My guess is that the action of the operator on the state vector [itex]\left|\psi\right\rangle[/itex] will collapse the vector to a single basis vector of p [itex]\left| p \right\rangle [/itex] the expression above would reduce to an element of a basis transformation matrix [itex]\left\langle x | p \right\rangle [/itex]

    Is that correct...at least in part?
     
    Last edited: Oct 9, 2012
  2. jcsd
  3. Oct 9, 2012 #2

    dextercioby

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    Not quite. The action of p on the ket psi leads to a ket phi, generally different. Then the matrix element with the bra x leads to a complex number, namely phi(x).
     
  4. Oct 10, 2012 #3
    Thanks for the reply.

    What would the physical interpretation of the complex number phi(x) be? The wavefunction of the state with eigenvalue of p?
     
  5. Oct 11, 2012 #4

    dextercioby

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    No, it's a generic wavefunction. No relation to spectral values of p.
     
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