All Questions
Tagged with electromagnetism operators
36
questions
2
votes
1
answer
440
views
Electron photon interaction - commutation of $\mathbf{A}$ and $\mathbf{p}$
I'm trying to figure out the radiative transition rates between electronic levels due to EM radiation using FGR as done by Merzbacher, this online source, and others.
I have two questions regarding ...
- 695
1
vote
2
answers
807
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Quantization of the Hamiltonian of a particle in a uniform magnetic field
If a particle of mass $m$ and charge $q$ is subject to a uniform magnetic field and if we have a vector potential $\mathbf{A}$ then we know that classically the dynamics of the particle will be ...
- 36.4k
12
votes
1
answer
3k
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Lorentz force derivation in quantum mechanics [closed]
In Sakurai and Napolitano, chapter 2, there's a derivation of the QM Lorentz force.
Given $$H=\frac{1}{2m}\left(\mathbf{p}-\frac{e\mathbf{A}}{c}\right)^2+e\phi = \frac{\mathbf{\Pi}^2}{2m}+e\phi$$
...
- 877
4
votes
1
answer
5k
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Operator algebra for momentum and magnetic vector potential
Let $\vec{A}$ be the magnetic vector potential and $\vec{p}$ be momentum.
$$ \vec{p} \cdot \vec{A} \psi = (\vec{p} \cdot \vec{A}) \psi + \vec{A} \cdot (\vec{p} \psi) $$
$$ \vec{A} \cdot \vec{p} \psi =...
- 427
9
votes
2
answers
3k
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Why is the "canonical momentum" for the Dirac equation not defined in terms of the "gauge covariant derivative"?
The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor <...
- 1,445
7
votes
3
answers
3k
views
Lorentz force in Dirac theory and its classical limit
It is well known that in Dirac theory the time derivative of $$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(...
- 2,335