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Homework Help: Expectation values

  1. Jan 11, 2007 #1
    How much sense does it make to compute expectation value of an observable in a limited interval? i.e.

    [tex]\int_a^b \psi^* \hat Q \psi dx.[/tex]
    rather than
    [tex]\int_{-\infty}^{\infty} \psi \hat Q \psi dx[/tex]

    Apparently, it shouldn't make any sense for it gives weird results when you compute e.v. of momentum for a part of infinite potentital well (say well is [0,a] and you do the e.v. integral from [0,a/3]]). Why do we have to integrate over all the space then?
     
  2. jcsd
  3. Jan 11, 2007 #2

    dextercioby

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    In the position representation, [itex] \psi (x) [/itex] is well defined on all real axis, even though the system might be constrained to "move" in a box.

    Daniel.
     
  4. Jan 31, 2007 #3
    you must integrate over entire space!
    For infinite potential, there in no leak for
    wavefunction beyond the potential boundary.
     
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