- #1

Niles

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## Homework Statement

Hi all.

When riding home today from school on my bike, I was thinking about some QM. The general solution to the Schrödinger equation for t=0 is given by:

[tex]

\Psi(x,0)=\sum_n c_n\psi_n(x),

[/tex]

where [itex]\psi_n(x)[/itex] are the eigenfunctions of the Hamiltonian. We know that the probability of [itex]\Psi(x)[/itex] collapsing to one of the eigenstates is given by the absolute square in front of that particular eigenstate.

Now my

**question**comes: Let's say we have an arbitrary operator Q: [itex]Q\psi_n = q_n\psi_n[/itex], where q

_{n}are the eigenvalues. Now what do I do if I want to find the probability of [itex]\Psi(x)[/itex] collapsing to one of the eigenstates of the operator Q upon measurement of the observable Q?

My

**own attempt**is that we write [itex]\Psi(x)[/itex] as a new linear combination of the eigenstates of Q. But to me this seems very difficult.

I hope you can shed some light on this. Thanks in advance.

Niles.