What does show solutions to the schroedinger eqn mean?

[Kovalainen]

What does "show solutions to the schroedinger eqn" mean?

I'm sorry for the very beginner question, I'm a mature student who's just come back to University so I'm unaccustomed to the terminology.

The question has given us a wave function and asked us to show that at later times Ψ is a solution to the schroedinger equation.

Is all I need to do plug it in and show that LHS = RHS?

 

[Octonion]

If they ask specifically for $\psi$ at later times then I'm guessing you may want to find the parts of $\psi$ that become negligible for large t. Then plugging in it should work.

 

[nnnm4]

You're right. Write down the initial state, and then the time-dependent wave function, plug it into the Schrödinger Equation, it make sure it holds identically.