# Questions tagged [operators]

Questions about using or composing operators--functional mappings from one state or vector space to another.

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### Why is the square of a differential operator not evaluated automatically?

I defined an operator: py[f_[x, y]] := (I*h*D[f[x, y], y] - x) // Expand (not important, but it represents a simplified component of a quantum momentum in a ...
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What would be the best way to define the Moyal Product, $f(x,p)\star g(x,p)$, in Mathematica? $f(x,p)\star g(x,p)$ may be written as $f\star g=\sum\limits_{n=0}^{\infty}\frac{1}{n!}\left(\frac{i\hbar}... 1answer 691 views ### Gâteaux (directional) derivatives and higher order differentials of a functional I would like to calculate the Gâteaux derivative of a functional (i.e. a function depending on functions). A simple example for the Dirichlet functional:$L(u(x))=\int_0^1 \frac{1}{2} (u'(x))^2 dx$... 4answers 2k views ### Exponential of a Differential Operator In Mathematica, is it possible to exponentiate a differential operator such that the operator will act on a function,$f(x,p)$? Specifically, I wondering if I can get Mathematica to do this:$\exp(c\...
What is the scalar product operator for complex vectors (or matrices) in Mathematica? The usual $Dot[]$ doesn't work. E.g. here is what the Mathematica gives $$\{1,0\}.\{I,0\}=I$$ but the answer ...