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11.7 General solutions

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

- $\displaystyle {\frac{\hbar^2}{2m}}$$\displaystyle \hat{\vec{p}}^{2}_{}$f (r) = - $\displaystyle {\frac{\hbar^2}{2m}}$$\displaystyle {\frac{1}{r^2}}$$\displaystyle {\frac{\partial}{\partial r}}$$\displaystyle \left(\vphantom{r^2 \frac{\partial}{\partial r}f(\vec{r})}\right.$r2$\displaystyle {\frac{\partial}{\partial r}}$f (r)$\displaystyle \left.\vphantom{r^2 \frac{\partial}{\partial r}f(\vec{r})}\right)$ + $\displaystyle {\frac{1}{r^2}}$$\displaystyle \hat{\vec{L}}^{2}_{}$f (r). (11.34)



© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk