- #1
gulsen
- 217
- 0
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?
[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?