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How do you Taylor expand [itex]e^{i \vec{k} \cdot \vec{r}}[/itex]
the general formula is [itex]\phi(\vec{r}+\vec{a})=\sum_{n=0}^{\infty} \frac{1}{n!} (\vec{a} \cdot \nabla)^n \phi(\vec{a})[/itex]
but [itex]\vec{k} \cdot \vec{r}[/itex] isn't of the form [itex]\vec{r}+\vec{a}[/itex] is it?
the general formula is [itex]\phi(\vec{r}+\vec{a})=\sum_{n=0}^{\infty} \frac{1}{n!} (\vec{a} \cdot \nabla)^n \phi(\vec{a})[/itex]
but [itex]\vec{k} \cdot \vec{r}[/itex] isn't of the form [itex]\vec{r}+\vec{a}[/itex] is it?