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11.7: General solutions

Last updated

Nov 4, 2024
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- 11.6: Spherical Harmonics
- 12: Quantum Mechanics of the Hydrogen Atom

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One of the reasons for playing such game is that we can rewrite the kinetic energy as

$-\frac{\hbar^2}{2 m} \hat{p}^2 f(\boldsymbol{r})=-\frac{\hbar^2}{2 m} \frac{1}{r^2} \frac{\partial}{\partial r}\left(r^2 \frac{\partial}{\partial r} f(\boldsymbol{r})\right)+\frac{1}{r^2} \hat{L}^2 f(\boldsymbol{r})$

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