Fundamental Process of an electron absorbing a photon

[Abu Abdallah]

Hello
I was thinkng of this question and I found it best expressed in a clear manner in another site. I quote the question and waiting for an asnwer:
"Is it a fundamental property of electrons that they can absorb photons?
Geometry requires that two points define a straight line. Geometry does
not prove this; it requires this. Does physics require that electrons can
absorb photons, or can physics prove this. Can the system be explained in
terms of the building blocks that combine to form electrons. A tank
destroys buildings. To explain how, we must define what the tank does to
the bricks and then define how this affects the entire building. Why do
we assume that the reaction between an electron and a photon can be
explained at the level of the entire electron. I want to know how does an
electron absorb a photon at the level of the actual reaction; at the level
of the bricks. Can we define the precise interaction between a photon and
some part of an electron at the moment that they merge. Entropy and
energy have no place here. Such terms are used to define the likelyhood
of an event occurring; not in the mechanism? If we had a magical
microscope through which we could view the process yet not affect the
process, what would we see?
A thoughtful answer deserves my most sincere thanks."

Another question in the same realm how does a discharge electron give its kinetic energy to the atom colliding with it and excite it to an excited state similar to what happens in a fluorescent lamp?

 

[lalbatros]

Abu Abdallah,

To answer your title question is easy.

An electron is a charged particles.
A photon is an electromagnetic wave.

When a charged particle is exposed to electromagnetic wave, it is set into motion by the electric field of the wave. The magnetic component of the electromagnetic wave can also modify the motion of the charge. This is simple classical electromagnetism.

When the intensity, dimension and time involved brings the physics in the quantum domain, this process takes a new aspect, from quantum mechanics. But the main aspect doesn't change: the electron can absorb energy from the electromagnetic wave. But, since now this can only go by quanta, either no absorption or total absorption of the photon will take place. This will occur at random. The physics takes a statistical aspect while preserving the classical laws in the average.

For the details of your message, I cannot answer yet because it was difficult for me to find a precise question that I could answer.

I would however advise you to avoid analogy in physics Analogy can be helpful for teaching but not really for understanding. For the electron/photon system the best analogy (to answer your question) is that of a boat in an harbor. When waves come from the see, the boat receives energy from the waves. Note that for the quantum aspect, it will be difficult to find any analogy.

I would also invite you to learn about the scientific method. Developments in physics have mainly started with the emmergence of the scientific method. Therefore, in physics, every knowledge must be based on experimental data and must be verified experimentally. Everything that cannot be verified experimentally, at least in principle, has no meaning for a physicist. In the last centuries in physics, new theories have been introduced mainly to correct and improve previous theories. The new theories have then been able to correct disagrement with older theories and often to predict new results and stimulate the invention of new experiments to make further checks. The interaction between photons and electrons has been verified in the greatest details you could imagine.

Altough I am not a specialist in the electron-photon interaction, I have worked in plasma physics in the past. Plasmas are completely ionised gases. Therefore, plasma physicists are very familiar with the interaction of charged particles and electromagnetic fields, but mostly in the domain of classical physics.

For example, the absorption of electromagnetic waves launched by RF antennas into a plasma is very well know in plasma physics, it is a daily reality in laboratories. I could cite many different applications of this classical EM-wave-electron interaction, like plasma heating and many different plasma diagnostics.

There is however at least one example I know in plasma physics where the quantum aspects come into play: it is the so-called "bremsthralung". In hot plasma, colliding electrons do emit (or create as opposed to "absordb"!) X-ray photons, and because of that they slow down. These X-rays are of course emitted as photons and these photons are detected/counted individually in the laboratories because this give a measure of the temperature. This phenoma is very well known and used as a plasma diagnostic tool. Other physicist have the same familiarity with the photon absorptions by electrons. These are all experimental fact described successfully by physical theories.




Michel


PS
About why and how.
In science and particularly in physics answering why and how only lead to new whys and hows. Why does an apple fall: because the Earth attracts it. But why does the Earth attracts if: some description in general relativity but now answer.
I think the main discovery of science is about asking the right questions questions that can be verified experimentally. But since our human experience will always be limited, our knowledge will also be limited.
Since the last centuries the number of answers has grown impressively. And so did the questions too. Is this freedom not marvelous?

 

[Abu Abdallah]

Michel,
I think that your point of view has a lot of supporters specially between expermentalists. It may seem fair that whatever cannot be put in an experiment nowadays shouldn't be questioned. But I believe that asking questions for better understanding always has a benefit. New 'good' questions that may lead to new theories refine our understanding of the universe and expose us more to the greatness of God in fabricating his creatures. Even if this hows and whys are not accessible to our measurement today, a day may come when the tools necessary to examine them have been developed. I think that the truth is always accessible to human beings. Of course, we will not be able to understand everything, but the level that we undestand correctly will be always, I hope, accessible to us. If this is not the case, why God has invited us to look into his heavens and and the Earth and whatever exists between them to discover his greatness ? * Not only that, but the proper answer to these questions ,I think, may lead to new technologies.

Regarding the scientific method, I invite you if you are interested to have a look at one of the very early founders of the scientific method : Ibn Al-Haytham

Without question, the greatest name in physics during the Arab/Islamic Empire was Ibn al-Haytham, born in the city of Basra, Iraq, in 965 A.D. By the time he died in 1030, he had made major contributions to optics, astronomy and mathematics, some of which would not be improved upon for six centuries.
Ibn al-Haytham's main field of interest and the one to which he made his greatest contributions, was the branch of physics we call optics. Striking parallels exist between his work and that of the seventeenth century English physicist, Isaac Newton, one of the greatest scientists of all time.
One of Newton's major accomplishments was his famous Law of Universal Gravitation. The most significant aspect of this theory is that it considers gravitation to be universal; that is, the same laws apply in the heavens and throughout the universe as apply on earth. This contradicts the idea held from the time of Aristotle (384-322 B.C.) that there is a difference between the laws governing events on Earth and those pertaining to celestial bodies. Newton realized that the force that causes an apple to fall from a tree is the same force that holds the moon and all the planets in their orbits and, indeed, is the same as that which governs the motion of the stars themselves.
If this idea were considered new in the seventeenth century, it was certainly new in the eleventh. Yet some of Ibn al-Haytham's experiments showed that he, too, believed that extraterrestrial phenomena obeyed the same laws as do earthly ones.
Ibn al-Haytham evolved his theories of optics through the study of light rays, and his investigations revealed a number of important properties: that light travels in a straight line; that every point of a luminous object radiates light in every direction; and that light weakens as it travels from its source. He studied these characteristics of light from a variety of light sources, i.e., self-emitting (the moon and reflecting bodies on earth).
This seemingly trivial experiment is in fact an early example of what is known as the "scientific method." Ibn al-Haytham designed an experiment to test a hypothesis, namely, that light travels in a straight line. His experiment was arranged to avoid the possibility of the experimenter's bias affecting the conclusions. Today, it seems obvious that light travels in straight lines, yet there was a time when intelligent men thought it obvious that the sun travels arounthe earth. The most advanced and sophisticated theory in modern physics, the Theory of Relativity, is derived from a refutation of ideas that are based on our everyday experience. Performing experiments to test and verify theories is at the heart of all modern scientific methods.
Ibn al-Haytham's experiments have even greater significance. By using the sun, the moon, lamps, fires and a variety of other light sources in his experiments, he was saying that light is light, regardless of its source. In this sense, he anticipated the universal laws of seventeenth century scientists.
We have described only the simplest of Ibn al-Haytham's experiments on the properties of light rays, but there are many others that were considerably more sophisticated. Ibn al-Haytham foresaw the works of later scientists not only in his use of experimentation but in the use of instrumentation: devices to help make measurements, the key to all modern science. He designed and constructed a variety of instruments, pipes, sheets, cylinders, rulers and plane, concave and convex mirrors in order to conduct his tests.
In addition to his studies of reflection, he also studied refraction, a phenomenon in which light rays bend when traveling from one medium to another, such as from air to water. The effect causes an object to appear to be in a location other than where it actually is, making him the first scientist to test a property of refraction that seems so obvious today. He demonstrated that a ray of light arriving perpendicular to the air-water boundary was not bent at all and showed that this was true for light passing through not just two, but several media. Clear parallels exist between his work and that of Isaac Newton six centuries later: both men studied that effects of light passing through glass, and both realized that the accepted ideas of their day were wrong.
It is difficult to appreciate the degree of intellect required by both these men to overcome the ingrained prejudices of previous centuries. The greatest scientists of Newton's day could not accept his theory of colors, a theory that we in the twentieth century, with three hundred years of hindsight, regard as self-evident. Newton's seemingly simple idea was that the colors produced when sunlight passes through a prism are caused by the separation of the sunlight, which contains all colors, into its constituent parts by refraction. Ibn al-Haytham demonstrated that the prism made the colors visible by bending rays of different colors in varying amounts, thus producing the familiar spectrum.
Ibn al-Haytham's explanation of how a lens worked required a similar leap of intellect. He contended that magnification was due to the bending, or refraction, of light rays at the glass-to-air boundary and not, as was thought, to something in the glass. He correctly deduced that the curvature of the glass, or lens, produced the magnification; thus, the magnifying effect takes place at the surface of the lens rather than within it.
This distinction is, of course, critical to the design of lenses, and without the ability to design lenses, we would have no cameras, movies, television sets, satellites, eyeglasses, contact lenses, telescopes, or microscopes—life would be very different for the human race.
Although he did not build a telescope, it is known that Ibn al-Haytham did construct parabolic mirrors. incoming parallel rays of light, such as those from the stars, are focused at a point so that such mirrors can be used to obtain unblurred images of celestial bodies and remote objects on the earth. Today, these are used in the world's great telescopes.
Like Newton, Ibn al-Haytham was interested in vision. Three Greeks, Galen in particular, did pioneering work on the anatomy of the eye and its connections to the brain, but did not produce a satisfactory theory of vision. Hero and Ptolemy both believed that vision was produced by the emission of light from the eyes, but their theory did not provide a reasonable explanation of perspective, the effect whereby the apparent size of an object depends upon its distance from the observer. As we know today, and as Ibn al-Haytham understood in the eleventh century, vision results from light being reflected into the eye from the object observed, an idea that explains perspective. He correctly regarded the eye as an intercepting screen, comparable to those we use today to show movies or slides. When his revolutionary ideas on perspective passed into Europe during the Renaissance, they influenced the development not only of science but also of art. The use of improved knowledge of perspective to give a feeling of depth and movement became strikingly visible in the works of Italy's new school of painters, the Perspectivi, around 1500.
Furthermore, Ibn al-Haytham appreciated that an explanation of vision must take into account not only such physical factors as light, screens, lenses and so on, but also anatomical and psychological factors, and he realized that the eye must function in a manner consistent with the laws of optics.
Ibn al-Haytham proved that the perception of an image occurs not in the eyes but in the brain and that the location of an image is largely determined by psychological factors. Like Newton, Ibn al-Haytham considered the problem of why a visual image produced within the brain is perceived as if it were located at some distance from the viewer, is the actual position of the object which produced it. Even today, most people do not find this surprising, although it is quite remarkable that images of the objects we see do not appear to be inside the head, where they actually exist, since they are simply electro-chemical versions of the scene inside the brain.
Ibn al-Haytham was aware of an even more subtle aspect of vision, namely, that when we see an object the brain automatically performs a memory retrieval procedure to see if it recognizes the object. The signals ultimately produced within the brain by light entering the eye cannot tell us that what we see is, for example, a loaf of bread. Almost instantly, the brain scans its memory and compares the new information it has received through the eyes with data it has stored over the years. Ibn al-Haytham called this function of the brain "the distinguishing faculty" and realized that it is intimately tied to the entire process of seeing.
That someone in the eleventh century realized that such complex questions existed is in itself noteworthy, but Ibn al-Haytham did not merely raise them, he attempted to provide answers. Explanations of these phenomena required him to construct a psychological theory of vision at a time when psychology was not recognized as a field of study. These ideas were quite different from the notions held by the Greeks and even by other contemporary Arab scientists.
The manner in which Ibn al-Haytham presented his theories in his Book of Optics is extremely interesting to the historian of science. He was both a mathematician and an experimenter, which allowed him to present his arguments with a power unmatched by previous scientists who rarely had experimental evidence to back up their assertions. Here lies another parallel between Newton and Ibn al-Haytham: they were both mathematicians and experimenters who made significant contributions to optics and other physical sciences by applying their knowledge of mathematics to the results of experiments. Ibn al-Haytham's descriptions of his experiments are replete with mathematical explanations in the form of geometric drawings, and he must have prepared engineering drawings or sketches to assist with the manufacture of his instrumentation.
About one-fourth of Ibn al-Haytham's more than 200 books and treatises survive; the best known of which is his Kitab al-Manazir, or Book of Optics (literally, Book of Perspectives). The breadth of the other subjects discussed in his book shows the wide range of his interests. They include optical illusions, the structure of the eye, binocular vision, perspective, atmospheric refraction, comets, mirages and the camera obscura. He is known to have studied physiology, anatomy and meteorology. Ibn al-Haytham also made notable contributions to astronomy. For example, he pointed out problems with the model of planetary orbits proposed by Ptolemy in the first century A.D., a model that was not superseded until the time of Copernicus in the sixteenth century.
It is not too much to claim that Ibn al-Haytham was not only the founder of the science of optics, but a pioneer in the modern scientific method and a man whose work stood unchallenged for six centuries before others were able to carry forward ideas that sprang from his fertile mind.

Thanks a lot for your reply.

Seeking a better understanding:
Abu Abd Allah

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* See quran- (29) verse 20, (10) verse 101, (7) verse 185

 

[lalbatros]

Abu Abdallah,

I don't think experimentalist are the main supporters of this point of view. Actually they play one special role in the scientific process: they concentrate on the experimental part, which also require a lot of creativity. It is true that theoreticians tend apparently to be more imaginative. But looking more closely, their imagination cannot escape the experimental facts that they must fit in the theories.

This does not mean that questions should be limited to current technical capacities. The Bell's inequalities are a nice example. The Bell inequalities, when they were published, offered for the first time the possiblity to check quantum mechanics against classical views of physics. It took sometimes before it was accessible to experience. In the first years, some took it as science-fiction. Other examples, from "big science" are even more striking.

However, the history of physics has shown that only reasonnable steps can be successful. The history of physics contains no record of theories totally disconnected from previous theories. On the contrary. Take quantum physics for example: it is striking to see how much it relies on classical physics, still it is maybe the boldest step in the history of physics. It makes no sense, indeed, to make theoretical proposals or models that would be totally out of reach of experience. Not only because of the experimental challenge. Actually, I believe, it is doubful that any physicist would be able to imagine theories that would be very far from current experimental reality. (altough one or two centuries could conceivable) The reason is clear: valid theories should anyway be connected to past theories and experimental data and therefore new theories are always extensions of previous knowledge. Therefore it is reasonnable to believe that the experimental steps needed to check a new theory should also be limited.




Michel

Postscriptum

Personally I have been educated as a Christian and I have turned to a tolerant atheist.
My personal feeling is that science invites us to forget about God and religion, for experimental reasons.
However, it maybe possible that mankind cannot live in a decent way without religion. But how could this theory be tested? What is our experimental background in this respect?
I do hope people can live in peace and love by nature.

 

[Severian]

Is it a fundamental property of electrons that they can absorb photons?

Like all good questions, the answer to this is yes and no. It depends on what you regard as an electron. One can describe an electron rather well using the Dirac equation, with or without an electromagnetic potential. In this set-up, no it is not a fundamental property because the interaction is put in by hand.

However, if you take the point of view that the electron is a representation of the group local U(1), then it is a fundamental property. One finds that the Dirac equation (or the Lagrangian it is derived from) is not invariant under the symmert group, and one has to postulate a new particle to restore its symmetry. This new particle is the photon, and its interaction with the electron is given. So the requirement of local U(1) derives the fundamental property in the question.

 

[ZapperZ]

Before things go into that much deeper, please keep in mind that the discussion in here must only be confined to strictly physics discussion. Whether it is relevant or not, and whether you like it or not, there shall be no references to any religious connotations, similarities, evidence, agreement, contradictions, history, etc.. etc.. Not only is this the wrong subforum for such discussions, but I will also point out specifically to the PF Guidelines that everyone has agreed to.

If you cannot carry a physics discussion without invoking religious context, then you have come to the wrong forum. This rule is not negotiable.

Zz.

 

[actionintegral]

I thought that a photon required an harmonic oscillator to be created or annihilated because a photon has a frequency. This would make me think that a free electron could not absorb a photon unless it were embedded in an harmonic oscillator ( like an atom or something).

 

[rlduncan]

I agree actionintegral, but could you elaborate on the nature of the harmonic motion for the ground state electron of the h-atom.

 

[actionintegral]

No! I can't! I start with the Schroedinger equation for the harmonic oscillator, and I see that it's energies are quantized. To me that is the origin of the photon. Then I take that concept and suppose that there is something about the structure of the hydrogen atom that is approximated by an harmonic oscillator.

 

[Worzo]

1) It's true. A free electron cannot absorb or emit a photon because spin is not conserved.

Photon (spin 1) + Electron (spin 1/2) = Electron (spin 1/2) + ...?

The only answer to the ...? part is that this must be a photon as well. Photons can be scattered by electrons, but "absorption" cannot occur.2) A hydrogen atom is not approximated by a harmonic oscillator. The hydrogen atom is approximated by a central potential. One origin of the photon is the electric dipole interaction, which is an oscillation of the electron's wavefunction between the quantized energy levels of this central potential.

EDIT: Sorry, I should clarify. An atom can be approximated as a harmonic oscillator, for example in the Einstein model of a solid, but this is for the purposes of determining the thermal properties of the atom. In terms of the interaction between the electron and the hydrogen atom, it is a central potential approximation.

 

[actionintegral]

2) A hydrogen atom is not approximated by a harmonic oscillator. The hydrogen atom is approximated by a central potential. One origin of the photon is the electric dipole interaction, which is an oscillation of the electron's wavefunction between the quantized energy levels of this central potential.[/QUOTE]

Thanks - I will read up on that.

 

[ZapperZ]

EDIT: Sorry, I should clarify. An atom can be approximated as a harmonic oscillator, for example in the Einstein model of a solid, but this is for the purposes of determining the thermal properties of the atom.

Even that isn't accurate even for thermal properties, since in solid, the Einstein model has been replaced with the Debye model.

Zz.

 

[Severian]

1) It's true. A free electron cannot absorb or emit a photon because spin is not conserved.

Photon (spin 1) + Electron (spin 1/2) = Electron (spin 1/2) + ...?

The only answer to the ...? part is that this must be a photon as well. Photons can be scattered by electrons, but "absorption" cannot occur.

Spin is a vector quantity, so the vector $$\vec{J}_e +\vec{J}_\gamma$$ has no problem having length 1/2 (e.g. $${J_z}_e =-1/2$$ and $${J_z}_\gamma=1$$)

You are confusing two issues. You are correct that an on-shell electron cannot absorb a photon (a second phton is required), but this is because of momentum conservation, not spin.

 

[masudr]

The photon is an excitation of the EM field. The Hamiltonian for the EM field has parts which correspond (roughly) to the kinetic and potential parts of the harmonic oscillator.

Thus using the ladder operator formalism for harmonic oscillators (but replacing the terms to match the corresponding Hamiltonian) we get creation and annihilation of photons at particular points in spacetime at particular frequencies. Q.E.D. (couldn't resist)

 

[actionintegral]

The photon is an excitation of the EM field. The Hamiltonian for the EM field has parts which correspond (roughly) to the kinetic and potential parts of the harmonic oscillator.

Yes, I looked at the schrodinger equation for a hydrogen atom and saw no mention of harmonic oscillators. Harmonic oscillators didn't come up until they discussed the EM wave. Then they magically appeared because we chose to describe an arbitrary EM waveform by harmonic oscillator frequencies.

I would suppose that if you chose another set of waveforms to describe your EM field, you would use a different type of "photon".

 

[lalbatros]

actionintegral,

The stationary modes of a rectangular cavity are really harmonic oscillators.
This occurs because of how harmonic waves propagate in such cavities.
It is clear that in the limit of very large cavities, it doesn't play any role that it is rectangular.
Thefore it appears naturally in QED.

michel

 

[actionintegral]

Hi lalbatros,

Please comment on my reasoning:

There are many solutions to the wave equation. One such solutions is simple harmonic motion. These are called "photons". Any solution to the wave equation can be formed by superposition of these "photons".

The choice of the simple harmonic motion solutions to the wave equation was arbitrary. Any complete and linearly independent set of solutions could have been chosen, giving rise to quanta of a different nature than
SHM photons.

 

[lalbatros]

Hi actionintegral,

Linear superpositions of normal modes are not normal modes.
This means that they are not stationary, the wave amplitude varies in time at the beating frequency(ies). By a suitable combination you could even create a field pulse. Such a pulse is always made of many photons=quanta.

Michel

 

[actionintegral]

There is no a priori reason to declare normal modes as the fundamental solution of the wave equation, except for their simplicity. You could consider square-wave pulses as the fundamental solutions, and create normal modes from a linear superposition of these.

Applying this to the schrodinger equation, aren't I free to define my "photons" as square wave pulses, and claim that your "normal mode" photons are really just superpositions of my "true" photons?

 

[actionintegral]

10 characters

 

[SF]

When an alectron absorbs a photon, it doesn't "eat" it like pacman would, instead, the photon's energy is absorbed by the electron which in turn jumps to a higher orbital in the atom.

 

[rlduncan]

2) A hydrogen atom is not approximated by a harmonic oscillator. The hydrogen atom is approximated by a central potential. One origin of the photon is the electric dipole interaction, which is an oscillation of the electron's wavefunction between the quantized energy levels of this central potential.

Yes, a photon is emitted or absorbed when the electron jumps between the quantized energy levels but what is responsible for the electric dipole configuration in the central potential model.

 

[Worzo]

Yes, a photon is emitted or absorbed when the electron jumps between the quantized energy levels but what is responsible for the electric dipole configuration in the central potential model.

Quantum mechanics shows that the electron does not "jump" once from one energy level to another: the wavefunction has a time-varying probability of being in the first energy level and the second energy level. This probabiltiy oscillates between the two levels whilst gradually moving from one level to the other.

A helpful (although not exact) analogy is to think of it like dropping a bouncing ball onto a table. When you are holding it above the table, it's in the higher energy state. Then when you drop it, it bounces lower and lower until it eventually ends up in the lower energy state.

Classicaly, it's this "bouncing" of the electron between the states that produces electromagnetic waves through the acceleration of the charge.

 

[Farsight]

Is it a fundamental property of electrons that they can absorb photons?

No. In simple terms, electrons do not absorb photons. Electron bonds absorb photons.

 

[rlduncan]

A helpful (although not exact) analogy is to think of it like dropping a bouncing ball onto a table. When you are holding it above the table, it's in the higher energy state. Then when you drop it, it bounces lower and lower until it eventually ends up in the lower energy state.

On the surface this seems to be a reasonable explanation, but what causes the electron to change directions as it oscillates back and forth and decays to the lower energy state. There must be a force acting on the electron to cause such periodic motion. Where does this force originate? Ellaborate on the electric dipole interaction mentioned earlier. What evidence do you have for this?

 

[samalkhaiat]

There are many solutions to the wave equation. One such solutions is simple harmonic motion. These are called "photons". Any solution to the wave equation can be formed by superposition of these "photons".

The choice of the simple harmonic motion solutions to the wave equation was arbitrary. Any complete and linearly independent set of solutions could have been chosen, giving rise to quanta of a different nature than
SHM photons.

There is no such thing as SHM-solutions. We just expand the field in plane-wave solutions. First year postgrad. students use this to prove that "free EM field" is EQUIVALENT to an "infinite but denumerable" set of "uncoupled" harmonic oscillators. This powerful "classical" result reduces the quantization problem of fields to that of simple harmonic oscillator.

Photon introduced by canonical quantization is identical to the photon introduced by path-integral quantization. The world would a very strange place if the nature of the field quanta depends on the method of quantization!
The interpretation of the EM field in terms of photons (QFT) is achieved by quantizing the individual oscillator modes.

regards

sam

 

[masudr]

Force? In quantum mechanics? What next?!

 

[Worzo]

On the surface this seems to be a reasonable explanation, but what causes the electron to change directions as it oscillates back and forth and decays to the lower energy state. There must be a force acting on the electron to cause such periodic motion. Where does this force originate? Ellaborate on the electric dipole interaction mentioned earlier. What evidence do you have for this?

OK, the analogy was a bad one for that reason. It's not helpful to think of a bound electron (as in an atom) as a particle. There is a wavefunction describing the probability of finding the electron in a certain place, if you wanted to look. It's this probability distribution that oscillates. That's the only way you can describe it.

A spontaneous emission of a photon like this is not actually "spontaneous". Atoms are always coupled, no matter how weakly, to the other atoms around them. Any small perturbation to the atom may cause the electron to jump down an energy level. It is this perturbation which sets the oscillation going.

 

[Meir Achuz]

A spontaneous emission of a photon like this is not actually "spontaneous". Atoms are always coupled, no matter how weakly, to the other atoms around them. Any small perturbation to the atom may cause the electron to jump down an energy level. It is this perturbation which sets the oscillation going.

The decay is indeed spontaneous. A completely isolated excited atom will decay.

 

[Abu Abdallah]

What about the second part of my message, regarding the excitation of atoms by discharge electrons? Any help about the details of this process?
lalbatros, please check your private messages.

 

[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. Schrodinger 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 absorbtion 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