- #1
MostlyHarmless
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Homework Statement
Show that the wave function ##\Psi(x,t)=Asin(kx-ωt)## does not satisfy the time dependent Schrodinger Equation.
Homework Equations
##-\frac{\hbar}{2m}\frac{\partial^2\psi(x,t)}{{\partial}x^2}+V(x,t)\psi(x,t)=i\hbar\frac{\partial\psi(x,t)}{{\partial}t}##
The Attempt at a Solution
So first step is I plug in the wave function:
##-\frac{\hbar}{2m}\frac{\partial^2Asin(kx-ωt)}{{\partial}x^2}+V(x,t)Asin(kx-ωt)=i\hbar\frac{{\partial}Asin(kx-ωt)}{{\partial}t}##
From here, I have a differential equation, which, I'm pretty sure I can't solve, but I'm mostly going off the fact that the question says to show that this wave function "does not satisfy.."
But I'm really unsure on how to show this..I don't remember a lot from DiffEq, but I can see that I can't do separation of variables here.