All Questions
Tagged with electromagnetism operators
37
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What are the operators here and how are these formulas derived? [closed]
In (23), are grad and div some kind of scalar operators comparing to $\nabla$ and $\nabla\times$? because tbh I dont know how $\text{curl}(\mu^{-1}\text{curl}\textbf{A})$ turns into $\text{div}\mu^{-1}...
- 103
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Derivation of the quantization of the EM field in a dielectrics
I'm currently studying the quantization of the EM field in a dielectric medium and trying to understand the quantization scheme of Huttner and Barnett (1992, see Phys. Rev. A 46, 4306). The system ...
1
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1
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63
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Canonical and kinetic momenta vs gauge dependence
I am struggling a bit to understand the concept of gauge invariance/dependence with canonical momentum.
For instance, if we consider a Hamiltonian of a particle in an electromagnetic field described ...
- 11
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1
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64
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set? [closed]
Copy from here https://mathematica.stackexchange.com/questions/284809/why-does-the-minimum-eigenvalue-change-dramatically-when-one-basis-function-is-a
I have a basis set which describes with high ...
- 233
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3
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Understanding of Legendre Polynomials
For some background, I transferred into physics from bio without taking hs precalc/ physics.
In my E&M lecture notes (not homework), my professor introduced the equations:
$$ \int_{-1}^{1} P_l (x) ...
- 21
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1
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413
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What exactly does it mean by gauge-invariant "operators"?
For simplicity, let us consider $U(1)$ gauge theory without matter fields.
At classical level, the gauge field $A^\mu$ has the gauge transformation law
\begin{equation}
A^\mu \to A^\mu +\partial^\mu \...
- 1,665
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2
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473
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Series expansion of unitary operators in terms of other operators
I am reading lecture notes on local gauge invariance, part of Prof. Ethan Neil's course on Quantum Mechanics at the University of Colorado.
There, he writes about introducing a so-called comparator $U(...
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2
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The operator calculation of Helmholtz equation?
I am reading the beam propagation method (BPM) in optical imaging paper. I find a paper solve the Helmholtz equation in the inhomogeneous media. The paper is:
Light propagation in graded-index optical ...
- 11
1
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1
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Expectation value of $ Y \otimes I \otimes I $ for a charged particle in a magnetic field
Typically when solving a Hamiltonian of ye olde form $ \frac{1}{2m} (\bar P - \frac{q}{c} \bar A)^2 $, you do separation of variables.
For simplicity say that $ A = - B Y \hat x $.
You can rewrite it ...
- 182
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51
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How to prove that momentum eigenstates are also eigenstates of asymmetric Landau Hamiltonian?
$$H(B,E)=\frac{1}{2m}p_x^2+\frac{1}{2m}\left(p_y-\frac{q}{c}Bx\right)^2-qEx$$
This Hamiltonian commutes with $p_y$, therefore, $\langle y|k_y\rangle=e^{ik_yy}$ are eigenstates of $H$, but how can I ...
- 97
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284
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Is there a (semiclassical) electric field operator?
So I come from a chemistry background, where the electronic structure of atoms and molecules is central. For practical purposes, we usually work with a charge density operator
$$ \hat{\rho}(r) = q \...
user312272
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126
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Ehrenfest theorem: On which classical circle can we find the electrons in an homogenous magnetic field?
In the French wiki article about the Ehrenfest theorem I found these formulas.
$${\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\langle {\hat {x}}\rangle ={\frac {1}{m}}\langle {\hat {p}}\rangle }...
- 678
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Quadratic Expansion With Operators [duplicate]
I was looking at the hamiltonian of a particle confined to the $x$-$y$ plane when it has mass $m$ and charge $q$ coupled to the electromagnetic field. My question is actually a very simple one. During ...
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590
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How to understand the time reversal symmetry of position operator?
How to understand the fact that position operator is symmetric under time reversal? I can visualize the momentum and magnetic field being odd under time reversal.
Got the same doubt for Electric field ...
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How does the electromagnetic dipole operator appear in the decay $b \rightarrow s \gamma$?
I was analyzing the effective theory of the process $b \rightarrow s \gamma$ and and I was in doubt about the emergence of the effective operator of photon dipole
$$O_7 = e m_b \bar{s}_L \sigma_{\mu\...
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