All Questions
Tagged with electromagnetism operators
36
questions
1
vote
1
answer
341
views
Minimal coupling Hamiltonian
A charged particle in an em field can be described by the following Hamiltonian (in CGS units):
$$H = \frac {(\vec{p} \ + \frac {q}{c}\vec{A})^2}{2m} + U(r)$$
But... what does it mean to square the ...
- 1,644
2
votes
1
answer
170
views
How to prove that the normal mode eigenvalue problem constitutes that of a Hermitian operator?
I am physics PhD student working on quantisation of electromagnetic fields in a non-homogeneous media. I am working through a paper at the moment and I am struggling with one of the statements. In the ...
3
votes
2
answers
483
views
Is electric field operator in Schrödinger picture time-dependent?
We know that in the Schrödinger picture, operators are time-independent if they do not have explicit time-dependence.
So do electric field and vector potential field operators have time dependence in ...
- 1,369
1
vote
0
answers
56
views
Why is there an inconsistency between the gauge transformation of the classical canonical momentum and the momentum operator in quantum mechanics? [duplicate]
I feel that there is a little inconsistency between the canonical momentum of a
classical charged
particle in an electromagnetic field and the momentum operator associated to the equivalent quantum ...
- 31
1
vote
1
answer
149
views
Schrödinger equation for charged particle in potential
This might be a silly question, but I don't think it is trivial.
I am trying to solve an example for my class. In it the Schrödinger equation for a charged particle in a vector potential is given:
$$i\...
- 1,488
3
votes
2
answers
593
views
The strange character of operator $\nabla$
I was first introduced to the mathematical operation gradient, divergence and curl not in Mathematics but during my studies of Electromagnetism. As you all know learning Maths from a Physics teacher ...
user240696
0
votes
1
answer
98
views
Evaluation of Hamiltonian of a charged particle under EM field
The Hamiltonian of a charged partical in EM field is given by $$H = \frac{\pi^2}{2m} -e \phi$$ where $$\boldsymbol{\pi}=-\mathrm{i} \hbar \boldsymbol{\nabla}+e \mathbf{A}.$$ To evaluate $\pi^2$, we ...
0
votes
1
answer
120
views
Justification of dropping term in Hamiltonian and expectation Values
While reading Sakurai's Modern QM, I was stuck at the point where he explains the absorption and emission of light quanta in atoms. He proceeds with Hamiltonian:
$$H= p^2/2m + e\phi(x) -e/mc A\cdot p$...
- 129
1
vote
1
answer
69
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An electrodinamic identity: starting point [closed]
With this request, I would like to ask you kindly how you can prove this identity. I thank you for those who can help me.
\begin{equation}
\overline{\nabla} \times (\overline{\nabla} \times \...
- 2,547
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#...
- 135
1
vote
1
answer
69
views
What is the physical interpretation of the derivative of a particle field?
I am learning quantum field theory, specifically the quantization of the electromagnetic field. We have this Laplacian
$$
\mathcal{L} = -\frac{1}{2} \partial_\mu A_\nu \partial^\mu A^\nu -j_\mu A^\mu
$...
2
votes
0
answers
144
views
What this quantum field operator represents $ b_{in}(t) = \frac{1}{\sqrt{2 \pi}} \int e^{-i \omega t} b(\omega)$? [duplicate]
In
Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation Physics Department, Uniuersity of Waikato, Hamilton, ¹tuZealand (Received 29 ...
- 1,450
0
votes
1
answer
252
views
Why do we think that the relation $\vec{\mu}_L=\frac{e}{2m_e}\vec{L}$ will be valid in quantum mechanics?
Assuming the electrons to revolve round the nucleus in circular orbits and using the fact from classical electromagnetism that a current loop behaves like a magnetic dipole of dipole moment $\vec{\mu}...
- 11.8k
1
vote
2
answers
327
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Problem with the Landau gauge
I'm having a very simple problem which probably has an equally simple answer. I'm following the wikipedia article: https://en.wikipedia.org/wiki/Landau_quantization
We have a uniform magnetic field ...
- 849
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} ...
- 6,601