All Questions
5
questions
2
votes
2
answers
111
views
Dirac delta of operators multiplying matrix element
In playing around with the Wigner-Weyl correspondence, I found myself needing to perform an integral of exponential operators, which I am confused about. TLDR: help to evaluate $$\int d{x}dy\ \delta(x\...
- 173
3
votes
0
answers
74
views
Are Wigner functions of any Unitary operator in $B(L^{2}(\mathbb{R}))$ in $L^{2}(\mathbb{R}^{2})$?
Are Wigner functions of any Unitary operator in $B(L^{2}(\mathbb{R}))$ in $L^{\infty}(\mathbb{R}^{2})$?
i.e.
Let $e^{iA} \in B(L^{2}(\mathbb{R}))$. Define the Wigner function (Wigner transform) as ...
- 90
1
vote
1
answer
192
views
Wigner-Weyl transform for a function of coordinates only
I am reading this paper by Tatarskii, which serves as an introduction to the Wigner representation of quantum mechanics.
There is a step in the paper involving the Weyl transform that does not seem ...
- 1,242
4
votes
1
answer
441
views
Non-commutative Fourier transform of an operator
Wigner-Weyl transform relates an operator to its distribution function in phase space through an operator Fourier transform which is said to be non-commutative.
$$
\hat{\rho} \xrightarrow[non-comm]{...
- 199
1
vote
2
answers
172
views
Basic confusion with quantum mechanical operators
Given a classical observable, $a(x,p),$ Weyl quantization gives the correspondent QM observable as:
$$\langle x | \hat{A} | \phi \rangle=\hbar^{-3}\int \int a \left(\frac{x+y}{2},p\right)\phi(y) e^{2\...
- 1,262