Remeasurement of a quantum system

[swain1]

After making a measurement of a particular dynamical variable the wavefunction collapses into the corresponding eigenfunction. As I understand when the variable is then measured again the results and relative probabilities of eigenvalues are exactly the same as before. I don't understand why they are the same as before. What happens to the wavefunction?

 

[actionintegral]

I think it slowly starts spreading out again.

 

[swain1]

ok. Why does it spread out though? Is there a reasoning behind why the eigenvalues will be the same when another measurement is made. There was a question in a book that kind of asked for an answer to this but I can't work out why?

 

[Epicurus]

Information. Start out with a state described by an eigenfunction then apply the propogator to it which describes the time evolution. At a later time the probability of observing some state is proportional to the overlap integral between the initial and final state...to put it simply