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Expectation values

  • Thread starter gulsen
  • Start date
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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?
 

Answers and Replies

dextercioby
Science Advisor
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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.
 
113
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you must integrate over entire space!
For infinite potential, there in no leak for
wavefunction beyond the potential boundary.
 

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