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Imagine I want to make a laser of electrons like a laser of light. Is that possible, or does the Pauli exclusion principle prohibit that?

Qmechanic
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Marijn
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    I think this shows a lack of Google fu. Free particles don't have quantised energy levels so the EP doesn't apply to them. See also on this site Is “microbunching” in a free electron laser limited by the Pauli exclusion principle? though that has only one (downvoted) answer. – John Rennie Jun 30 '16 at 11:09
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    @JohnRennie We have a semantic issue. Exchange symmetry applies to free electrons. So the question is whether or not the exclusion principle is the same as exchange symmetry. (I usually think of them as being the same thing.) – garyp Jun 30 '16 at 11:14
  • The comments you got involve the Free Electron Laser, https://en.wikipedia.org/wiki/Free-electron_laser which gives off a coherent photon beam. They point out that since potentials are involved specific energy levels will appear and for those energy levels the Pauli exclusion would limit the number of electrons on each level, except that within the variables in magnetic field we can reach in our labs this is not attainable. Are you asking about a coherent beam of electrons? – anna v Jun 30 '16 at 12:13
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    Yes, it is about a coherent beam of electrons. The FEL is a stream of photons caused by electrons, but that is not the question. – Marijn Jun 30 '16 at 13:01
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    @John Rennie: what do you mean the exclusion principle doesn't apply to free particles? Do all the neutrons in a neutron star live in quantized energy levels, or does the Pauli exclusion principle not help keep neutron stars from collapsing under gravity? The real question is how strong an electron beam needs to be for it to apply. (And how to produce this electron beam, since standard techniques for lasers only work on bosons.) – Peter Shor Jun 30 '16 at 23:41
  • @RobJeffries I included this link in the answer that was accepted – anna v Oct 25 '20 at 09:22
  • Good old Coulomb repulsion will impose a limit on the focussing of an electron beam. – my2cts Oct 25 '20 at 10:18

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This is almost a duplicate then of Pauli exclusion principle in an electron beam. Almost because it asks about cathode ray beams. The answer there is yes; the Pauli exclusion principle plays a role similar to the neutron star role.

For an accelerator beam, where the electrons and positrons are considered free particles, as were the LEP e+ e- beams, the effect has not been considered as far as I can see. As the other answer states, there is no time constraint in such beams.

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anna v
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Lasers operate via the stimulated emission of light. This is a phenomenon that applies to bosons, since the stimulated photon is in the same state as the photon that stimulates it.

The same thing cannot happen in fermions; instead there is an analogous process called stimulated absorption which means that the intensity of a fermion beam would be decreased whilst travelling in the "lasing medium". Thus, no amplification.

If on the other hand you are just asking whether degeneracy imposes a limit on the density of an electron beam where the electrons have a narrow range of momentum, then the answer is yes and is handled by the duplicate.

ProfRob
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Yes, you can make an electron beam. And the Pauli exclusion principle doesn't prohibit it.

According to the Pauli exclusion principle, two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously. Here you may have missed the word simultaneously. An electron can have the same position in space (all quantum numbers same), but at different times.

Peter Mortensen
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Shubhansh Awasthi
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    The Pauli exclusion principle really will prevent a beam of electrons from being too strong, because the electrons can't overlap in momentum/position space. (Position alone doesn't come into the Heisenberg uncertainty principle.) However, I think we're a very long way from that point with experimental electron beams right now. – Peter Shor Jul 02 '16 at 11:21
  • You cannot make a thick high density beam with electrons only a very thin one because Pauli. – Markoul11 Aug 12 '22 at 09:08