Time independent wave function vs the initial wave function

[iScience]

I thought there was a difference, but I'm being told now that the time independent wave function is the wave function at t=0

 

[andrewkirk]

Are you sure you mean time independent wave function? The words 'the time independent' in my experience are usually used to preface either 'Schrödinger equation' or Hamiltonian. The time-independent Schrödinger equation is just the Eigenvalue equation for the Hamiltonian operator: $H|E>=E|E>$ and where the Hamiltonian is time-independent, the solutions of this, together with the initial state expressed in terms of those eigenkets, and an easily-identified propagator, are all that is needed to give the wave function at any future point in time.