Wave particle duality as applied to photon

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Wave-particle duality indicates that matter behaves as both a particle and a wave, with quantum mechanics (QM) providing a statistical interpretation of this phenomenon. Photons, like electrons, are treated as quantum mechanical particles in probabilistic terms when observed individually. In large quantities, photons can be described using classical electromagnetic wave theory, unlike matter particles, which are fermions and cannot occupy the same state. The discussion raises questions about reconciling the concepts of matter waves and electromagnetic waves, particularly regarding the nature of photons. Understanding this duality remains a complex aspect of quantum mechanics.
ArielGenesis
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so basically a wave particle duality principle state that sometimes a "matter" would behave as a particle and a wave a another time. The was to reconcile this is through QM's statistical interpretation and the math construct is very obvious that such proposed matter is indeed a wave-particle in duality. The wave is a matter wave or probability wave.

Now my question is, how about light, or photon. Is it an EM wave or a probability wave?
 
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The situation with the photon is the same as with the "matter" particle like electron.
 
When we have a single photon (or a "few" of them) we must deal with it as a QM particle (which is different from a classical particle) in probabilistic terms.

When we have bazillions and bazillions of photons, as we do in most "everyday" situations, we can describe their combined effects in terms of classical electromagnetic waves.
 
jtbell said:
When we have bazillions and bazillions of photons, as we do in most "everyday" situations, we can describe their combined effects in terms of classical electromagnetic waves.
It is interesting to note that we cannot do that for matter particles, because matter particles are fermions so you cannot have many fermions in the same state. A more technical way to say this is that fermions cannot be in a coherent state.
 
so, a single photon cannot be described as an EM wave?

I mean I fully understand the idea that particle is a matter-wave. I am doing QM so it is pretty familiar.

The problem is I that I cannot yet reconcile the idea that a matter wave is an EM wave as well. I have no idea what that means.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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