# Serious conceptual problem with QM (eigenfunctions)

The wavefunction psi is often separated into two parts, the time dependent part and the part which has only spatial dependence (phi), and this I think can only be done if we assume that the potential is not a function of time. I often see proofs where we have H acting on phi (not psi) and we get H (phi1) = E1*phi1. However this equation is essentially just the TISE, which of course only applies for time independent potentials. Does this mean that we should generally assume that the potential is not a function of time while working with eigenfunctions of different observables?

Also, does the potential not being a function of time essentially the same as having an isolated system?

Sachi

time indep.: No, not in general. Time-dependent perturbation theory is the first counterexample I thought of.

dextercioby
Homework Helper
sachi said:
The wavefunction psi is often separated into two parts, the time dependent part and the part which has only spatial dependence (phi), and this I think can only be done if we assume that the potential is not a function of time.

If the Hamiltonian is explicitely time independent, we can factorize the time-dependence of the state vactor into an exponential containing the spectral values of the Hamiltonian.

Sachi said:
I often see proofs where we have H acting on phi (not psi) and we get H (phi1) = E1*phi1. However this equation is essentially just the TISE, which of course only applies for time independent potentials. Does this mean that we should generally assume that the potential is not a function of time while working with eigenfunctions of different observables?
Also, does the potential not being a function of time essentially the same as having an isolated system?
Sachi

Isolated systems involve (at classical level) the absence of external force fields. The only possible interactions are the internal ones which are generally time independent...

Daniel.