- #1
Old_sm0key
- 17
- 0
Homework Statement
I'm asked to show that the two dimensional plane wave (for constant C)
[tex]\psi \left ( \mathbf{r} \right )=Ce^{-i\mathbf{k}\cdot \mathbf{r}}[/tex]
satisfies the Schrödinger equation:
[tex]-\frac{\hbar^{2}}{2m_e}\frac{\mathrm{d}^2 \psi\left ( \mathbf{r} \right )}{\mathrm{d} \mathbf{r}^2}=E\psi\left ( \mathbf{r} \right )[/tex]
but I'm flummoxed by differentiating wrt a vector, [itex]\mathbf{r}[/itex]. Can someone explain how I should understand this differential, so that I can produce the required equality?
Thanks in advance.