Schrodinger and Infinite Square Well hell

[shyguy79]

Schrödinger and Infinite Square Well... hell

Homework Statement

Show that Schrödinger Equation: $\frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0$ has the solution $\psi(x)=A\sin(kx)$

Homework Equations

$k=\frac{\sqrt{2mE_{tot}-E_{pot}}}{\hbar}$

The Attempt at a Solution

I already know that $\frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0$ is a differential equation and has a solution $\psi(x)=A\sin(kx)$ but it's just something learned as fact. How do I go about showing it?

Any pointers would be appreciated... thanks in advance!

 

[rshalloo]

Generally solving differential equations involves knowing general solutions such as the one you've shown. If you wanted to prove it you could just simply sub it into your differential equation and prove that it does indeed satisfy the equation. I.e differential psi twice and add it with (k^2)*psi

 

[shyguy79]

Thank you.. Just needed a kick in the right direction... Didn't even need to use the value of k.