(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

With [itex]\vec{L}[/itex] = -i[itex]\vec{r}[/itex] x [itex]\nabla[/itex], verify the operator identities

[itex]\nabla = \hat{r}\frac{\partial }{\partial \vec{r}}-i\frac{\vec{r}\times\vec{L}}{r^{2}}[/itex]

and

[itex]\vec{r} \bigtriangledown ^2 - \bigtriangledown (1+\vec{r}\frac{\partial }{\partial \vec{r}})=i\bigtriangledown \times \vec{L}[/itex]

2. Relevant equations

3. The attempt at a solution

... I tried to expand it, and use some identities... But the equation becomes super complicated... Help!

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# Curvilinear Coordinates and Vector Calculus

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