- #1

- 274

- 3

This is driving me mad:

[itex]\hat{\vec{\nabla}}(\hat{\vec{A}})f=(\vec{\nabla}\cdot\vec{A})f + \vec{A}\cdot(\vec{\nabla}f) [/itex] for an arbitrary vector operator ##\hat{\vec{A}}##

So if we set ##\vec{A} = \vec{\nabla}## this should be correct

[itex]\hat{\vec{\nabla}}(\hat{\vec{\nabla}})f=(\vec{\nabla}\cdot\vec{\nabla})f + \vec{\nabla}\cdot(\vec{\nabla}f) = 2\vec{\nabla}^2f[/itex], but apparently its not. Why?

I mean, ##grad( div(f)) = div(grad(f)) = \Delta f##, right?

Where did I go wrong?