Classical vs Quantum Electromagetism

[LarryS]

I'm having trouble relating the classical (Maxwell) model for electromagnetic radiation to the quantum mechanical (Q.E.D.) model. How do the magnetic field wave and electic field wave components of the classical electromagnetic wave relate to the quantum mechanical wave function for a photon?

 

[Meir Achuz]

E and B are found from the QM A^\mu of a photon using the usual classical definitions.
A classical EM wave corresponds to N coherent photons, with N>>>1.

 

[Entropia]

The classical model of electromagnetism, as described by Maxwell's equations, is a macroscopic theory that describes the behavior of electromagnetic waves in terms of electric and magnetic fields. These fields are considered continuous and can be described by classical wave equations. On the other hand, the quantum mechanical model, known as Quantum Electrodynamics (QED), describes the behavior of electromagnetic interactions at the microscopic level, specifically for individual particles such as photons.

One of the key differences between the classical and quantum mechanical models is the concept of quantization. In the classical model, electromagnetic fields are continuous, but in the quantum mechanical model, they are quantized into individual particles, or photons. This means that the electric and magnetic fields are not continuous waves, but rather are made up of discrete packets of energy, each corresponding to a single photon.

In terms of the relationship between the classical and quantum mechanical models, it is important to understand that the classical model is an approximation of the quantum mechanical model. In other words, the classical model is valid for large-scale phenomena, where the effects of individual photons can be averaged out. However, at the microscopic level, the quantum mechanical model must be used to accurately describe the behavior of electromagnetic interactions.

To further understand the relationship between the classical and quantum mechanical models, it is helpful to consider the wave-particle duality of light. In the classical model, light is described as a continuous wave, but in the quantum mechanical model, it is described as both a wave and a particle. This means that the electric and magnetic fields of a classical electromagnetic wave can be thought of as the wave component of a photon in the quantum mechanical model.

In conclusion, while the classical and quantum mechanical models of electromagnetism may seem very different, they are both valid and necessary in different contexts. The classical model is useful for understanding macroscopic phenomena, while the quantum mechanical model is necessary for understanding the behavior of individual particles. The relationship between the two models is complex but can be understood through the concept of wave-particle duality.