Electromagnetism Quantization

In summary, the conversation discusses two formulas for transverse electric and magnetic fields, with epsilon being a unit vector orthogonal to kappa. The authors compute the commutator of these fields and find a term involving the partial derivative with respect to z. The question asks about the origin of this term and suggests a possible solution involving the Fourier transform.
  • #1
naima
Gold Member
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I start from these formulas(transverse electric and magnetic fields)
## E_\perp(r) = \Sigma_i i \mathscr E_{\omega_i}\epsilon_i [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##
and
##B(r) = \Sigma_i i(1/c) \mathscr E_{\omega_i}(\kappa_i \times \epsilon_i) [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##
where epsilon is a unit vector orthogonal to ##\kappa_i = k_i/|k_i|##.
The authors compute their commutator and write it as
##[E_{x \perp}(r),B_y(r')] = -i (\hbar/\epsilon_0) \partial_z \delta(r - r')##

I do not see where this ##\partial_z## comes from.
Have you an idea?

Is it related to FT(f'(z)) = i k FT(f(k))
 
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  • #2
I think that the solution is closer.
As ##\mathscr(E)_{\omega_i} = \sqrt{\frac{\hbar \omega_i}{2 \epsilon_0 L}}## and ##h \omega_i = |k_i| c##
I get in the commutator a ##-1/ \epsilon_0## and the ##|k_i|## disappears in ##\kappa_i## and i come closer to a "i z FT(f(z)" term.
Help will be appreciated!
 

What is electromagnetism quantization?

Electromagnetism quantization is the theory that describes the behavior of electromagnetic waves and their interaction with matter at the quantum level. It explains how electromagnetic radiation, such as light, is emitted and absorbed in discrete packets of energy called photons.

How does electromagnetism quantization relate to classical electromagnetism?

Classical electromagnetism describes the behavior of electromagnetic waves and their interaction with matter at the macroscopic level. It is based on continuous fields and does not take into account the discrete nature of energy at the quantum level. Electromagnetism quantization builds upon classical electromagnetism by incorporating quantum principles to explain the behavior of electromagnetic radiation on a microscopic scale.

What is the significance of electromagnetism quantization?

Electromagnetism quantization is an important concept in modern physics as it helps to explain many phenomena that cannot be explained by classical electromagnetism, such as the photoelectric effect and the behavior of atoms and molecules. It is also essential in the development of technologies such as lasers, transistors, and solar panels.

Who first proposed the concept of electromagnetism quantization?

The concept of electromagnetism quantization was first proposed by Max Planck in 1900. He introduced the idea of quantized energy levels to explain the emission of energy from heated objects, which laid the foundation for the development of quantum mechanics.

How is electromagnetism quantization used in modern research?

Electromagnetism quantization is used in a wide range of fields, including particle physics, condensed matter physics, and quantum optics. It is also used in the development of new technologies, such as quantum computing and quantum communication. Researchers continue to study and explore the principles of electromagnetism quantization to further our understanding of the quantum world.

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