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In what sense is $\breve{g}(x-y)/(2\pi)^n$ the integral kernel of $g(-i\nabla)$?
It is said in Trace Ideals and Their Applications by Barry Simon that the integral kernel of the operator $g(-i\nabla)$ on $L^2(\mathbb R^n)$ is given by $\breve{g}(x-y)/(2\pi)^n$.
Indeed, for any $\...
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0
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proof of the product: x times m derivative of delta function.
The question is in one dimension and is : Prove that $$x\delta^{(m)}=-m\delta^{(m-1)},\ m \in \mathbb{N},$$
where $\delta^{(m)}$ is the $m$-derivative of $\delta.$
As I know, I got through this way:
$...
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Scaled Dirac Delta function: $ \delta (xe^r - y) $
I was reading on squeezed Gaussian states and stumbled upon this paper:
Equivalence Classes of Minimum-Uncertainty Packets. II.
It is mentioned after Eq. $\left(2\right)$ that
$$
\left\langle x\left\...
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