Fundamental Process of an electron absorbing a photon

[actionintegral]

There is no such thing as SHM-solutions.

...

This powerful "classical" result reduces the quantization problem of fields to that of simple harmonic oscillator.

sam

Hi Sam,

Thank you for your response. But I am confused by what appear to be contradictory statements. Could you please clarify (using small words!)

 

[rlduncan]

Force? In quantum mechanics? What next?!

The problem with current quantum theory is the difficulty the mind has in grasping these seeming strange concepts. This is due to the lack of forces, particle properties, etc. Schrödinger said it best:

–that it seems not only dangerous but even desirable, for a time at least, to lay an exaggerated stress on its counterpart. In doing this we must of course realize that a thorough correlation of all features of physical phenomena can probably be afforded only by a harmonic union of these two extremes.
--E. Schrödinger

 

[SF]

Why would you call it a "problem" of the quantum theory? By this you suggest that it is flawed in some fundamental way that we (the others) cannot grasp.

The real problem is trying to explain the quantum world in terms of the classical world, but nature simply doesn't work that way.

 

[reilly]

If one goes back to the invention of QED, then it is clear that the idea of electron absorption and emission and electron-photon dynamics came ultimately from the "quantization" of classical electrons and Maxwell.

It was Dirac who, through extraordinary intuition and brilliance, figured out the ubiquitous three-point interaction, showed how to compute the transition probabilities for Hydrogen, and gave the tools for computations of the Compton Scattering cross-section ), electroproduction of electron-positron pairs. Of course, such luminaries as Heisenberg, Jordan, Pauli, Fermi, Weiskopf, Wigner, Oppenheimer and Furry played key roles in the early and later development of QED and QFT.

The plain fact is that absorption and emission of particles is a fundamental assumption of both QED and QFT. (I'm more than aware that free particles don't absorb or emit photons without other interactions present -- more photons, external fields. But, the matrix elements of emission or absorption of photons by a charged particle are generally not zero -- it's conservation laws that prohibit a free particle from absorbing or emitting a photon while remaining a free particle. Check it out, the matrix element for a hydrogen atom to go from a 1-S to a 2-P state while emitting a photon is not zero. The probability, on the other hand is slim to none-- unless the atom is not isolated.

Those who disregard history are doomed to repeat it. Many of the topics discussed in this forum were addressed many years ago -- as can be seen in such works as Weinberg's Chap I of Vol I of his QFT treatise, and Schweber's QED: and the Men Who Made It, and in Dirac's Quantum Mechanics -- of the three, Dirac's book is absolutely essential for becoming "fluent" in QM.

The plain fact is the the assumption of emission and absorption of photons is not really that much different than Maxwell's conclusion that acceleration of charged particles causes radiation -- we get the "how", but the why is not really explained classically or quantumly (sorry 'bout that). To use a current phrase, at the end of the day we do not really understand the why of electromagnetics, but we are pretty good at the how of it -- radar, Lamb-Shift, radio and TV, X-Rays, and so forth
Regards,
Reilly Atkinson

 

[samalkhaiat]

Hi Sam,

Thank you for your response. But I am confused by what appear to be contradictory statements. Could you please clarify (using small words!)

Hi,

By the first statement I implied the following:

1) the plane wave solutions do not represent harmonic oscillators.
2) they are not arbitrary, as they must satisfy the relativistic relation between energy and momentum.
3) all of the above is in the contex of classical field theory. i.e. No photons.

My second statement was about "one" particular method of quantization.
As I said before (sorry for not using small words ), by certain transformation on the field amplitudes, one can put the "classical" Hamiltonian in a form similar to that of infinite number of free oscillators. This makes life easy when we try to quantize the EM-field because, we know (from kindergarten QM) how to quantize oscillators.
One could use different quantization method, but the end result must not be different.

regards

sam

 

[actionintegral]

Got it - thanks!

 

[Abu Abdallah]

it's conservation laws that prohibit a free particle from absorbing or emitting a photon while remaining a free particle.

Reilly,
your reply was very informative. Conservation laws provide good reasons for us to understand why an interaction can happen or not, but for the particle itself I think there should be a more fundamental reason. The particle doesn't know that charge, for example , has to be conserved, but any possible interaction that the particle can go through should conserve charge. Take another example: a ball at rest on the ground doesn't go upwards by itself against gravity. We can say that's because the energy will not be conserved in this case, but the real reason that the charge understands is that there is no thing (force) that pushes it upwards, so why take the trouble? I know that this may seem useless for some people, but this is the level of understanding I aim to.

The plain fact is the the assumption of emission and absorption of photons is not really that much different than Maxwell's conclusion that acceleration of charged particles causes radiation -- we get the "how", but the why is not really explained classically or quantumly (sorry 'bout that).

I hope you elaborate on that. How can the process of producing photons classically- acceleration of charges- be similar to photon production in quantum mechanics- transition between different states.? I hope I can find a treatment that unifies both processes, since I think they should be two faces of the same process, the final products of them are the same: photons !


Abu AbdAllah

 

[actionintegral]

Revisiting

To me this was a good question because it made me think a lot.

The creation of a photon requires the "infrastructure" of an harmonic oscillator. I say this because I look at the shrodinger equation and it contains a macroscopic harmonic oscillator potential.

Therefore, it seems to me, that to absorb a photon, one must already have an harmonic oscillator in place. Whether the photon is absorbed by an electron or something else is secondary. The photon is absorbed by an harmonic oscillator.