Why does Asin(kx−ωt) not satisfy the time-independent Schrödinger equation?

[Skullmonkee]

Homework Statement

Show that the function $$\Psi(x,t)=Asin(kx- \omega t)$$ does not satisfy the time-independent Schrödinger Equation.

Homework Equations

Time independet SE

The Attempt at a Solution

I think i have to solve for derivative of $$\Psi(x,t)/t$$ and second derivative of $$\Psi(x,t)/x$$ but I'm not sure how to answer the question.

I attempted to differentiate the wave function with respect to time and space so that i got
$$\partial\Psi(x,t)/\partial t = -\omega Acos(kx-\omegat)$$
and that $$\partial^2\Psi(x,t)/\partial x^x = -kAsin(kx-\omegat)$$

If so, how do i prove that the original function does not satisfy the TDSE?

 

[Niles]

The time-independent Schrödinger equation says Hψ = Eψ, where E is the eigenvalue. The Hamiltonian will tell you what to differentiate with respect to.