Dear Prof. Ioannis Hadjidakis

From capture I see the 2 black marks pointing a whole wave package, isn´t it?

From [1] we can read that, I quote:

• "... a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit..."
• "...a wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere..."

[1] https://en.wikipedia.org/wiki/Wave_packet

So the answer is yes, it has a direct relation with the amplitude of the sinoid-wave of monochromatic light. The A(k) in wikipedia reference [1] and the u ( x, t ) in "basic behaviors part" description, these 2 equations relate the wave packet to a sinoid-wave. In addition, I can recommend a very good book on these questions: the Berkeley Physics Course Vol 3, Waves [2]:

[2] Waves (Berkeley Physics Course, Vol. 3) by Frank S. Crawford Jr.

I suggest that you take a look at group velocity in Wikipedia.

Everything said is definitively correct. However, I have some concern on something that could appear "semantic", but it is not so.

Just to launch a funny trick on the table...

consider the simplest case of a perfectly monochromatic lightwave propagating in vacuum. From a purely classical viewpoint, there would be no wavepackets, but just a plane wave with vp=vg=c... hence the parallelism photon=packet would loose any meaning.

This is the base difference between classical and quantum approaches to electromagnetic signal propagation: rigorously speaking, classical packets should not be intended as "photons", that instead are overlaps of "probabilty waves" of bosonic quantum states.

Dear Giuseppe,

You wrote: "From a purely classical viewpoint, there would be no wavepackets, but just a plane wave with vp=vg=c... hence the parallelism photon=packet would loose any meaning."

I agree with your prudence, in interpreting the behavior of single photons as being "wave packets" à la Quantum Mechanics.

From Maxwell's initial conclusions, electromagnetic energy involves by structure a "transverse" electromagnetic oscillation, which is completely absent from the concept of a wave packet, that are by structure entirely made of longitudinal waves. The same, it seems to me with classical longitudinal wave perpective

From my perspective, this can't be the answer

Best Regards, André

dear André,

I'm not sure to have well understood the point.. however, let me say in another way:

In vacuum, a monochromatic electromagnetic wave moves from a source to a receiver as a pure transverse EM wave, along the Poynting vector direction. Therefore, we agree that kind of signal is transmitted via a non-packeted wave ... At the same time, the same signal can be considered as a flux of monochromatic photons, which are "particles" in a quantum approach. My trick just referred to such a distinction, that seems to suggest that photons, as they are termed in QM, are not necessarily "wave packets", as they are termed in Classical Optics. As a consequence, in my opinion the parallelism "Photon - Energy Packet" included in the title of the post is, generally speaking, questionable.

Dear Giuseppe Curro

You wrote: " In vacuum, a monochromatic electromagnetic wave moves from a source to a receiver as a pure transverse EM wave, along the Poynting vector direction. Therefore, we agree that kind of signal is transmitted via a non-packeted wave ... At the same time, the same signal can be considered as a flux of monochromatic photons, which are "particles" in a quantum approach.

I agree.

Actually, a monochromatic electromagnetic "wave" in the classical sense involves the existence of some underlying medium if it can succed in propagating. The same for the traditional view of longitudinally propagating monochromatic photons.

Louis de Broglie however, proposed in the 1930's a solution for particle style monochromatic photons that could be self propelling from part of its energy while the other part is carried forward while in standing transverse electromagnetic oscillation that requires no underlying medium.

Although the traditional wave treatement is perfectly adequate from our macroscoscopic perspective, sort of treating energy as a flux of countless localized photons, the de Broglie quantized approach seems much more interesting at the subatomic level. Just like we treat water as a fluid without internal structure at our macro level, while knowing perfectly well that at the submicroscopic level, it is made of clearly identifiable separate molecules.

If interested in seeing what this de Broglie solution proposes, it is described here:

Michaud A (2016) On De Broglie’s Double-particle Photon Hypothesis. J Phys Math 7: 153. doi: 10.4172/2090-0902.1000153

https://www.gsjournal.net/Science-Journals/Research%20Papers-Mechanics%20/%20Electrodynamics/Download/5789

Best Regards, André

Dear Giuseppe ,

I thought, even monochromatic lightwave is propagating in vacuum through energy-packets (as well as classical waves). What do you mean by "purely classical viewpoint"? Light is wave AND particle (as far as I know). As wave is presented by the classical sinusoidal-wavefunction while as particle is presented by the energy-packets.

The point is that energy-packets could be the sum of two (or more/countless) wave-modes whose wave-functions accomplish certain relations and restrictions, in order to result the familiar final form of the figure shown. I wonder what these relations and restrictions are, for photon-energy to be the proper one (=h*c/λ) for any photon.

P.S. I agree that wavefunctions may be probability-waves, but their interpretation is beyond this thread.

Dear all,

You should know that the lowest energy photon ever detected had a few mm wave length (CERN)!

Longer waves comes from EM-radiation which is a separate phenomenon.

JES

Dear Giuseppe,

I have recommended your contribution because of its distinction between different physical levels of description. I want to add here a warning that de Broglie considered a `de Broglie wave' as a wave accompanying an individual object. Such de Broglie waves should not be confounded with quantum mechanical Schroedinger waves, which are statistical descriptions of ensembles, and hence have a completely different meaning.

Dear Willem Marinus de Muynck,

Note that the QM statistical description is Heisenberg's description that maps over Schrödinger's wave description. What Schrödinger contributed is a wave function that describes a resonance volume within which the electron momentum energy is deemed to be oscillating.

This is why the de Broglie pilot wave is conceptually related to the Schrödinger wave equation.

Both de Broglie and Schrödinger were opposed to the Heisenberg interpretation because it caused the neglect of research for a mechanical explanation of the transitions between orbitals in correlation with bremmsstrahlung photons emission and absorption.

If interested, this is analyzed at the beginning of this paper:

Michaud, A. (2018). The Hydrogen Atom Fundamental Resonance States. Journal of Modern Physics, 9, 1052-1110. doi: 10.4236/jmp.2018.95067

https://www.scirp.org/pdf/JMP_2018042716061246.pdf

Best Regards, André

Dear Ioannis Hadjidakis,

You wrote: "When a single photon is emitted by an electron transition between two energy levels, does it have a definite frequency?(certainly it HAS) Where is the/my fault?"

It certainly has, and also the corresponding wave length.

You can calculate its velocity with the 4th equation in the third column of Maxwell's equations table.

Best Regards, André