It is very well known result that ##grad[e^{i\vec{k}\cdot \vec{r}}]=i\vec{k}e^{i\vec{k}\cdot \vec{r}}##. Also ##\vec{k}\cdot \vec{r}=kr\cos \theta## and ##gradf(r)=\frac{df}{dr} grad r##. Then I can write(adsbygoogle = window.adsbygoogle || []).push({});

[tex]grad e^{ikr\cos \theta}=ik\cos \theta e^{i \vec{k}\cdot \vec{r}} \frac{\vec{r}}{r}=ik\frac{\vec{k}\cdot \vec{r}}{kr}e^{i\vec{k}\cdot \vec{r}} \frac{\vec{r}}{r}[/tex]

Somehow it is the same result only if ##\vec{k}=\frac{(\vec{k}\cdot \vec{r})\vec{r}}{r^2}## and this is not the same. Right?

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# A Gradient of scalar product

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