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7 questions
1
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1
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71
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Meaning of colon symbol $:$ in optics
When I was reading some early days nonlinear optics paper/textbooks (particularly between 1960-1985), I often see expressions such as:
$\chi^{(2)}:\textbf{E}\textbf{E}$
or
$\nabla\textbf{E}:\partial \...
- 173
0
votes
1
answer
132
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Vector calculus in Electromagnetism [closed]
I found a problem which had $$\partial_i (A_j \vec{G})= (\vec{\nabla} .\vec{ A} )\vec{G}+ (\vec{A}.\nabla) \vec{G} $$ but my problem is what does $$\partial_i (A_j \vec{B})$$ even mean? it doesn't ...
- 63
4
votes
1
answer
111
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What does $\mathbf{A}\cdot\nabla$ mean here?
What does $\mathbf{A}\cdot\nabla$ mean in an expression like $(\mathbf{A}\cdot\nabla)\mathbf B$?
I found this in Griffiths’ Classical Electrodynamics book and cannot figure it out.
0
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1
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1k
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Commutator of covariant derivative and field $F_{\mu \nu}$
I am working with the covariant derivative and trying to show that the commutator of this derivative
$[D_\mu , D_\nu]$ is proportional to the field $F_{\mu \nu}$. That is, I need the final term to
be ...
user276724
1
vote
2
answers
812
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Reason why dot notation isn't used for time derivatives in Maxwell's equations [closed]
Maxwell's equations seem to be usually written:
\begin{align}
\nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\
\nabla \cdot \mathbf{B} &= 0,\\
\nabla \times \mathbf{E} &= -\frac{\partial \...
user113773
0
votes
1
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953
views
Derivative with tensor indices
I have trouble figuring out derivatives in tensor notation in SR. I haven't been able to find a simple recipe for writing down a solution. For example what would be the solution to the following ...
- 3
4
votes
2
answers
271
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Conventions regarding partial derivatives
Look at this expression:
$$\frac{\partial}{\partial t} (V-\mathbf{v}\cdot\mathbf{A}).$$
This expression occurs in Griffiths EM book (4th ed, p.444). $V=V(\mathbf{r},t)$is the scalar potential, $\...
- 1,417