- #1

- 23

- 0

## Main Question or Discussion Point

I'm in my second year of a physics degree and my QM lecturer showed us how to calculate the RMS around the expectation of an operator by considering the E of a system in equal superposition of two energy eigenstates u_1 and u_2. He then says

"This gives some measure of how far oﬀ we would be likely to be from the expectation value for an average measurement. The general case for this can be derived. For an operator Q, then the wavefunction can be expressed as an expansion in eigenstates of Q " and writes the wavefunction as a sum over the eigenstates with coefficients whose modulus squared represent the probabilities of each eigenstate.

Could someone show me the derivation please?

Thanks!

"This gives some measure of how far oﬀ we would be likely to be from the expectation value for an average measurement. The general case for this can be derived. For an operator Q, then the wavefunction can be expressed as an expansion in eigenstates of Q " and writes the wavefunction as a sum over the eigenstates with coefficients whose modulus squared represent the probabilities of each eigenstate.

Could someone show me the derivation please?

Thanks!