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A laser is built on quantum mechanics to create a beam of photons with the same frequency and phase. Someone told me a free electron laser is a based on classical electrodynamics. Is that true?

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    $\begingroup$ Maybe relevant: aip.scitation.org/doi/abs/10.1063/1.34633 (basically yes, to a very good approximation) $\endgroup$ – Superfast Jellyfish Feb 25 at 10:00
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    $\begingroup$ FWIW, a free electron laser is not a LASER (i.e., not "Light Amplification by Stimulated Emission of Radiation.) It's a completely different mechanism for generating coherent light. $\endgroup$ – Solomon Slow Feb 25 at 13:11
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    $\begingroup$ Am I the only one who saw the title of this question and thought that were asking it it was possible to build a laser during the Classical Period (e.g. Ancient Greece)? $\endgroup$ – nick012000 Feb 26 at 11:52
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    $\begingroup$ @nick012000 No, I too thought this was going to be about something similar to Archimedes' death ray. $\endgroup$ – Mast Feb 27 at 10:56
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    $\begingroup$ There is this 1972 article (behind paywall :/) journals.aps.org/pra/abstract/10.1103/PhysRevA.5.1298 called "Classical Laser" by Borenstein and Lamb. The abstract contains "The conclusion is that laser action is not intrinsically a quantum-mechanical effect. " $\endgroup$ – EigenDavid Feb 27 at 12:38
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is classical laser possible?

IMO, the question doesn't make sense. "Classical" and "quantum" are not different options for how a thing can work. They are different options for us to try to understand how it works. LASERs aren't "built on" quantum mechanics, but rather, quantum mechanics is an appropriate tool for understanding stimulated emission. A free electron laser isn't built on classical electrodynamics, but classical electrodynamics offers a sufficient explanation for why it emits light.

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    $\begingroup$ I hear that, but certainly the fact that some quantum mechanisms do good job of explaining how a laser works suggests the question: "is there a classical mechanism that explains how a laser works?" $\endgroup$ – nomen Feb 25 at 19:04
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    $\begingroup$ Things can be built based on a certain framework in my opinion. So I interpret the statement “lasers are built on quantum mechanics” as a device that is built based on our understanding of quantum mechanics. There’s a difference between building something based on a framework and explaining something within a framework. $\endgroup$ – Superfast Jellyfish Feb 25 at 20:27
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    $\begingroup$ Sorry, -1. This is not an answer but rather a somewhat irrelevant statement about semantics. It is physically and logically meaningful to ask whether something is classical or quantum. There are some phenomena which are inherently quantum and some phenomena that can be perfectly understood from a classical physics standpoint. OP wanted to know if the free electron laser can be accurately described without using principles for QM. This is a well defined and clear question. Another phrasing could have been "should I care about the value of $\hbar$ if I want to build a free electron laser"? $\endgroup$ – MannyC Feb 27 at 21:57
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The crux of regular laser’s working principle is the population inversion of the lasing medium. This is a quantum property arising due to the discreteness of energy levels.

But when you have a free electron, quantum mechanically the energy spectrum is now continuous. So the electron no longer has to jump discretely and continuous change in the energy (parametrised by $\vec k$) is possible. Since the wavefunction can now readily expressed as a plane wave, the classical treatment of an oscillating charge with harmonic time dependence gives the same result.

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In the Wikipedia article

In most cases, the theory of classical electromagnetism adequately accounts for the behavior of free electron lasers.[11] For sufficiently short wavelengths, quantum effects of electron recoil and shot noise may have to be considered.

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