I am trying to understand why the collapse of the wave function can not be a solution to the Shroedinger equation. Certainly there are systems that evolve into eigenstates. For instance, in a two state system with constant Hamiltonian there are initial conditions from which the amplitudes oscillate back and forth and pass through eigen states periodically. In the Stern-Gerlach apparatus a magnetic field separates particles into spin directions.Blocking one of the directions with a barrier selects for the other spin eigen state. But all of this seems to be a solution of the Shroedinger equation.