- #1
shyguy79
- 99
- 0
Schrödinger and Infinite Square Well... hell
Show that Schrödinger Equation: \frac{d^{2}\psi(x)}{dx^{2}}+k^{2}\psi(x)=0 has the solution \psi(x)=A\sin(kx)
k=\frac{\sqrt{2mE_{tot}-E_{pot}}}{\hbar}
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!
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!