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4 questions
6
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4
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Is it possible to simplify this operator? Special case of Hadamard's formula
Let $D=\frac{d}{dx}$ be the derivative operator and $f(x)$ be a cubic polynomial. Is it possible to simplify the following differential operator? $T=e^{D^2}f(x)e^{-D^2}$.
I tried to use Hadamard's ...
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1
vote
1
answer
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Exponentiation of linear combination of commuting Vector fields proof other direction
I have already asked this question, but I forgot to include the if and only if. So the question has already been answered in one direction, but I have to prove the converse as well.
So If
$$e^{a\...
- 1,518
0
votes
1
answer
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Exponentiation of linear combination of commuting Vector fields
I have to prove the formula:
$$e^{a\partial/ \partial\lambda +b \partial / \partial\mu}=e^{a\partial/ \partial\lambda}e^{b\partial/ \partial\mu}$$
if $\partial/ \partial\lambda$ and $\partial/ \...
- 1,518
1
vote
4
answers
420
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What do $\nabla$ and $\frac{d }{d t}$ mean when they are by themselves?
In QM and QFT, I have seen some equations where they have just the derivative and/or the gradient without specifying what it is acting on.
Taken from wiki.
This does not make sense to me since I ...
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