All Questions
Tagged with electromagnetism operators
36
questions
5
votes
1
answer
287
views
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
$$ \hat{\rho}(r) = q \...
0
votes
0
answers
26
views
Derivation of the quantization of the EM field in a dielectrics
I'm currently studying the quantization of the EM field in a dielectric medium and trying to understand the quantization scheme of Huttner and Barnett (1992, see Phys. Rev. A 46, 4306). The system ...
1
vote
1
answer
63
views
Canonical and kinetic momenta vs gauge dependence
I am struggling a bit to understand the concept of gauge invariance/dependence with canonical momentum.
For instance, if we consider a Hamiltonian of a particle in an electromagnetic field described ...
0
votes
1
answer
64
views
Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set? [closed]
Copy from here https://mathematica.stackexchange.com/questions/284809/why-does-the-minimum-eigenvalue-change-dramatically-when-one-basis-function-is-a
I have a basis set which describes with high ...
1
vote
3
answers
251
views
Understanding of Legendre Polynomials
For some background, I transferred into physics from bio without taking hs precalc/ physics.
In my E&M lecture notes (not homework), my professor introduced the equations:
$$ \int_{-1}^{1} P_l (x) ...
1
vote
1
answer
429
views
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 \...
7
votes
3
answers
3k
views
Lorentz force in Dirac theory and its classical limit
It is well known that in Dirac theory the time derivative of $$P_i=p_i+A_i$$ operator (where $p_i=∂/∂_i$, $A_i$ - EM field vector potential) is an analogue of the Lorentz force:
$$\frac{dP_i}{dt} = e(...
1
vote
2
answers
480
views
Series expansion of unitary operators in terms of other operators
I am reading lecture notes on local gauge invariance, part of Prof. Ethan Neil's course on Quantum Mechanics at the University of Colorado.
There, he writes about introducing a so-called comparator $U(...
7
votes
1
answer
580
views
Why is the generalized momentum replaced by the momentum operator but not the ordinary momentum?
I was trying to understand the derivation of the Hamiltonian for a charged particle in an electromagnetic field. https://en.wikipedia.org/wiki/Hamiltonian_mechanics#...
1
vote
2
answers
182
views
The operator calculation of Helmholtz equation?
I am reading the beam propagation method (BPM) in optical imaging paper. I find a paper solve the Helmholtz equation in the inhomogeneous media. The paper is:
Light propagation in graded-index optical ...
2
votes
1
answer
146
views
How to prove that the quantity appearing in the exponent of the path integral is the Lagrangian?
In Zee's Quantum Field Theory in a Nutshell, it is shown that, if $H = \frac{\hat{p}^2}{2m}$, then
\begin{equation}
\langle q_F | e^{-iHt} | q_I \rangle = \int e^{i\int \frac{1}{2}m\dot{q}^2 \, dt} ...
1
vote
1
answer
121
views
Expectation value of $ Y \otimes I \otimes I $ for a charged particle in a magnetic field
Typically when solving a Hamiltonian of ye olde form $ \frac{1}{2m} (\bar P - \frac{q}{c} \bar A)^2 $, you do separation of variables.
For simplicity say that $ A = - B Y \hat x $.
You can rewrite it ...
0
votes
1
answer
51
views
How to prove that momentum eigenstates are also eigenstates of asymmetric Landau Hamiltonian?
$$H(B,E)=\frac{1}{2m}p_x^2+\frac{1}{2m}\left(p_y-\frac{q}{c}Bx\right)^2-qEx$$
This Hamiltonian commutes with $p_y$, therefore, $\langle y|k_y\rangle=e^{ik_yy}$ are eigenstates of $H$, but how can I ...
0
votes
1
answer
127
views
Ehrenfest theorem: On which classical circle can we find the electrons in an homogenous magnetic field?
In the French wiki article about the Ehrenfest theorem I found these formulas.
$${\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\langle {\hat {x}}\rangle ={\frac {1}{m}}\langle {\hat {p}}\rangle }...
0
votes
0
answers
31
views
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 ...