gulsen
Jan11-07, 08:23 AM
How much sense does it make to compute expectation value of an observable in a limited interval? i.e.
\int_a^b \psi^* \hat Q \psi dx.
rather than
\int_{-\infty}^{\infty} \psi \hat Q \psi dx
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?
\int_a^b \psi^* \hat Q \psi dx.
rather than
\int_{-\infty}^{\infty} \psi \hat Q \psi dx
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?