say we have some wavefunction |psi> and we want to find the probability of this wavefunction being in the state |q>. I get that the probability is given by P = |<q|psi>|^2 since we're projecting the wavefunction onto the basis state |q> then squaring it to give the probability density.(adsbygoogle = window.adsbygoogle || []).push({});

However what if we want to measure some observable quantity corresponding to some operator Q with one (of multiple) associated eigenstate |q>, and then find the probability that the system is in a state |q> after being observed. Would probability then be P = |<q|Q|psi>|^2 since I'm collapsing the wavefunction then projecting it onto the basis state |q>?

But say I didn't make a measurement of the system (not apply Q to |psi>) I get the original result. In these two cases I get a different answer do I not? In both cases I'm finding the probability of the wavefunction being in state |q>. Why are the answers different and what do |<q|psi>|^2 and |<q|Q|psi>|^2 fundamentally mean?

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# What's the difference between these two equations?

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