# Eigenfunction, Eigenvalue, Wave Function and collapse

1. Dec 29, 2007

### birulami

Reading Sam Treiman's odd quantum he nicely explains the dependencies between the Schrödinger wave equation, eigenvalues and eigenfunctions (page 86 onwards). In his notation, eigenfunctions are $u:R^3\to R$ and the wavefunction is $\Psi:R^4\to R$, i.e. in contrast to the eigenfunctions it depends on time.

Then on page 94 he says:
With "state of the system" he refers of course to $\Psi$, so during the measurement, the jump or collapse is from $\Psi$ to $u$.

The one thing I don't understand here is: $u$ does not depend on time, so how is the development of the new $\Psi$ over time governed? Is it that every solution of the Schrödinger equation is uniquely determined as soon as the value at just one point in time is known?

Harald.