(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

<O> = Int (from -inf -> inf) [(Psi*)O(Psi)] dx

3. 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*d^{2}/dx^{2}(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

A^{2}hbar^{2}k_{1}^{2}/2m + B^{2}hbar^{2}k_{2}^{2}/2m as this looks like an eigenvalue

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# Expectatoon value particle in superposition of momentum states

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