Schrodinger Equation and wavefunctions

[Chemist20]

not all functions are wavefunctions. For functions to be wavefunctions they have to obey a series of "rules". Now, my question is:

there are many functions, which obey these rules which aren't eigenfunctions of the hamiltonian, thereby meaning that they don't obey the Schrödinger Equation. Can systems described by these kind of wavefunctions exist or is it, as I think it is, not physically possible??

 

[Jano L.]

Hello Chemist20,

I do not think the psi-function has to be an eigenfunction of the Hamiltonian to describe the system in general. Many calculations deal only with such functions, but there are situations in which the psi-function cannot be of such nature; this is when the atom is under action of external forces. The wave function governed by Schroedinger's equation of motion then varies with time and is not an eigenfunction of the Hamiltonian. I think generally any differentiable and normalizable wave function is conceivable.