Of course, since they’re obviously proportional and both proportional to Planck’s constant.
The denominator of the Compton wavelength, λCompton = h/mc, is mc,
that of the de Broglie wavelength, λdB=h/p, is p = mvγ = mcβγ, where β=v/c and γ=1/(1-β2)1/2... So
λdB=λCompton/(βγ)
What matters is their meaning...Their relation isn't that interesting, because it isn't used anywhere...
Stam Nicolis
Thank you very much for the information. I study this subject for the electron. I study how when the electron is excited by quantized amount of energy, the electron can emit the mentioned energy in the form of a photon. But I'm not sure whether to include γ in the calculation because in my opinion the electron must re-emit exactly what it receives. The electron must indeed emit a photon whose energy must be exactly equal to the energy which the electron can receive knowing that the electron in my opinion can only receive quantified energies. I also ask myself if the "job" of the electron is to transform the energies he receives into photons? I ask myself if the electron is also a "transporter" of energies during the electronic transitions in an atom.Best regards.
Stam Nicolis
I mean the wave speed of the photon is the "c" speed of light, but I am trying to find out what should be the speed v of the wave associated with the electron as a particle according to de Debroglie. I consider that the electron has a radius (of the order of ten to the power ten minus nineteen fentometer fm), a frequency, an intrinsic energy, and also a mass.
Sorry I correct: ten to the power minus nineteen meter in place of "ten to the power minus nineteen femtometer".
Dear Jamil Kooli,
your questions in the last comment are not entirely correct. Уou must specify the conditions in which the electron is.
In atom the electron may absorb the incident photon, if during its transition on a higher energy level the electron will change direction of its spin to the opposite or its orbital momentum will increase by one. From my point of view this process corresponds to a transformation of one element (photon, as h=E/ν) of surrounding space to an element of inner space in the atom, being equal to h too. Sorry, but it is my own conception of discreet spaces.
Electron moving in a permanent magnetic field may emit a photon within the framework of bremsstrahlung effect. It means the electron disturbs an element h of the surrounding space in the form of photon.
Electron in free space may scatter an incident photon in two ways. One will be an elastic Compton scattering with photon energy change. It means that two quanta of action h were first united during interaction and then were separated after. The second way is photon scattering at small angles without its energy change. It looks like the photon is moving near the electron as in the electron-curved space.
Sincerely yours, Dulin Mikhail.
Dear Mikhail N Dulin
Many thanks for the reponse. I think that when the electron is totally excited it can emit a photon with an energy almost equal to mcc (m being the mass of the electron) at this time the wavelength of the emitted photon is slightly longer than the wavelength of the compton, but not equal. Best regards.
Jamil Kooli, be careful.
I don't know the term "electron is totally excited".
In the atom an excited electron will emit a photon with the energy of allowed transition or not emit if its energy will turn into heat due to a non-radiative process under interaction of the atom with the surrounding ones.
Mikhail N Dulin
For me when the electron receives a quantized energy (the electron is then excited) it then restores the energy received in the form of a photon but there is a certain limit. For me the electron can at most receive a quantity of quantized energy a little less than mcc (mc squared) and could emit a photon which wavelength is almost equal but not equal to the Compton wavelength. For me the electron can "store quantified energy in a "relativistic time" and "transport" it during electronic transitions in an atom. I have my theorie for the electron not yet published. I find that most of people do not understand well the de Debroglie equation. Finally you know no one has observed an electron!
Mikhail N Dulin
Sincerely I think that people who don't know how to calculate the intrinsic energy of the electron still have a lot to learn about this particle!
Dear Jamil Kooli,
I wish you good luck in the world of virtual particles.
Dear Mikhail N Dulin
Many thanks for your explication. Keep in touch. Best regards.
“Is there any relationship between the Compton wavelength and the de Debroglie wavelength of a particle?”
- the answer to the question above
- “…Of course, since they’re obviously proportional and both proportional to Planck’s constant.
The denominator of the Compton wavelength, λCompton = h/mc, is mc…λdB=λCompton/(βγ)
What matters is their meaning...Their relation isn't that interesting, because it isn't used anywhere........”
- looks as rather questionable. Really 1924 de Broglie wavelength hypothesis related to yet “Bohr’s motion” of electron along the orbit of H-atom, where de Broglie conjectured that that is happen as that electron at the motion forms standing waves with wavelength λ=h/p, p=mV is the electron’s momentum, V is its speed on the orbit. Further after in 1925-6 first QM version appeared that was generalized on any motion of any particles in the 3D Matter’s space.
In the mainstream physics that has no relation to the Compton wavelength, which is λC=h/mc, since in the mainstream momentums p=mcdon’t exist, particles cannot move with the speed of light.
Correspondingly the mainstream physics states, including, that if a particle is at rest in the 3D space, i.e. V=0, its DE Broglie wavelength is infinite, and so the particle exists with equal probability in all points of Matter’s 3D infinite space – what looks for any normal human as rather evident absurdity.
Such transcendent things are completely legitimate in the mainstream because of in mainstream philosophy and sciences, including physics, all really fundamental phenomena/notions, first of all in this case “Matter”– and so everything in Matter, i.e. “particles”, “fields”, etc., “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational,
- so completely logically inevitably, even in some banal cases, as the above one, and in all cases when mainstream addresses to really fundamental problems, the results is/are some transcendent, etc., consequences – as the above, or quite transcendent, etc., theories.
Real scientific explanation of what are the phenomena/notions above is possible, and is done, only in framework of the 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see
https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed
- and more concretely to what exists and happens in the informational system “Matter” in the informational physical model , which is based on the conception and is in complete accordance with all existent reliable experimental data, two main papers are
https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics, and
https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics .
In the model it is quite rationally postulated that the ultimate base of Matter is the primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4+1]4D dense lattice, which is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct), while everything in Matter, including particles, is/are some specific disturbances in the lattice.
The disturbances appear if some the lattice’s FLE is impacted by some momentum, so the disturbances further propagate with 4D velocities that have identical absolute values be equal to the speed of light, c, [“bold” is 4D vector] in the 4D space with metrics (cτ,X,Y,Z). Particles are close-loop algorithms that constantly cyclically run, having the momentums P=mcand energies E=Pc.
So really in Matter two types of particles exist: (i) – “T-particles” that are created by momentums’ components that are directed along the cτ-axis, if a T-particle is at rest in 3D space so it has “rest mass”, and (ii) “S-particles” that are created by momentums that are directed along some 3D line, so S-particles move only in 3D space having no rest mass, now physics knows really only S-particle “photon”.
Correspondingly in first approximation any particle at every time moment exists as some FLE-flipping point, which moves along corresponding 4D “helix”, radius of which is λ=ћ/P, which is directly photons wavelength.
Note here that in this case λisn’t a T-particle’s Compton length is defined only when it is at rest in space, and so m is m0, i.e. rest mass. Motion of T-particles in whole 4D space is more complex, including the de Broglie wavelength is the 3D projection of 4D “helix”, and the helix is a sum of two helixes with “axes” that are directed along the cτ-axis and 3D motion direction, however particle “occupies” always 4D space volume that has a characteristic “size” that is limited by the radiuses, i.e. Compton and de Broglie wavelengths above,
- including when a T-particle is at rest in 3D space, it by no means is “smeared in infinite space”, it occupies the volume with radius in the space that is equal to its particle’s Compton length.
More see the links above.
Cheers
Dear Jamil Kooli
Your question is very pertinent.
You have a clear understanding of most aspects of these processes.
For more info along this line of thinking:
The wavelength established by de Broglie is the wavelength of the energy induced at the mean ground state distance (the Bohr radius) of the hydrogen atom, whose equation was published in his 1924 thesis that allowed him to relate Planck's constant with the whole set of atomic resonant frequencies. It is different from the electron Compton wavelength by a factor α2 (the fine structure constant squared) and induces a theoretical classical velocity in the electron at the mean ground state distance of the hydrogen atom of c multiplied by α.
The manner in which Bremsstrahlung photons are emitted when electrons are captured in positively ionized atoms, or emitted when an over-energized electron returns to its rest orbital in an atom is analyzed in this article. All formal references are provided, with direct links for those that are available on the Internet:
Article On adiabatic processes at the subatomic level (Expanded repu...
Best Regards, André
Sergey Shevchenko
André Michaud
Many thanks for your explanations.
Because Compton's wavelength is a limiting value, Debroglie's equation is a wonderful equation because it gives intermediate states. But de Debroglie, in my opinion, failed to add another equation for the purpose of making his equation well related to Compton's wavelength equation to fully explain wave-particle duality. For the example of the electron for me this one when it is excited by a quantized energy it "spits" this energy in the form of a photon then the electron returns its initial state.
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