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Fixxxer125
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Homework Statement
Demonstrate the relation between the expectation value and the measurement outcomes of an observable of a particle by conisdering as an observable the kinetic energy operator
E=p^/2m when the particle is in a superposition of 2 momentum eigenstates
Homework Equations
<O> = Int (from -inf -> inf) [(Psi*)O(Psi)] dx
The Attempt at a Solution
I am taking the superposition of 2 momentum eigenstates as
Psi= square root (1/L) [ A*exp(ikx)exp(-iEt/Hbar) +B*exp(ikx)exp(-iEt/Hbar) ]
And then putting this into the integral
<O> = Int (from 0->L) [(Psi*)(-hbar/2m*d2/dx2(Psi)] dx
However I end up with a very long equation for the expectation value whereas I thought the expectation value would be something along the lines of
A2hbar2k12/2m + B2hbar2k22/2m as this looks like an eigenvalue