For measurement of any observable associated with the particle, should the wavefunction after collapse be a solution of the time-dependent Schrodinger equation?
A general solution of the time dependent schrodinger equation is given by superposition of eigenfunctions of the hamiltonian operator. Here by eigenfunctions, I mean the complete wavefunction as a function of spatial and time co - ordinates.
But since the wavefunction collapses to an eigenfunction of the operator of an obsevable when a measurement of the observable associated with the particle is made, What I want to ask is the following:
Should the collapsed wavefunction which is an eigenfunction of that operator be general solution of the Time - dependent schrodinger equation as well?