- #1
warfreak131
- 188
- 0
What does it mean to "satisfy" the Schrodinger equation?
Show that the 2p wave functions of the hydrogen atom satisfy the radial Schrodinger eq.
One of the radial equations for the 2p state is [tex]\frac{1}{\sqrt{96 \pi a^{3}}} \frac{r}{a} e^{\frac{-r}{2a}}[/tex]
[tex][\frac{-\hbar^2}{2m}\frac{1}{r^2}\frac{d}{dr}(r^2\frac{d}{dr})+\frac{l(l+1)\hbar^2}{2mr^2}+V(r)]R=ER[/tex]
I took the derivative with respect to r, and followed all the subsequent derivatives, and the answer is really messy. What exactly am I looking for when something "satisfies" the equation?
Homework Statement
Show that the 2p wave functions of the hydrogen atom satisfy the radial Schrodinger eq.
One of the radial equations for the 2p state is [tex]\frac{1}{\sqrt{96 \pi a^{3}}} \frac{r}{a} e^{\frac{-r}{2a}}[/tex]
Homework Equations
The Attempt at a Solution
[tex][\frac{-\hbar^2}{2m}\frac{1}{r^2}\frac{d}{dr}(r^2\frac{d}{dr})+\frac{l(l+1)\hbar^2}{2mr^2}+V(r)]R=ER[/tex]
I took the derivative with respect to r, and followed all the subsequent derivatives, and the answer is really messy. What exactly am I looking for when something "satisfies" the equation?