I know the wave nature of electrons was evoked to explain why atoms are stable but I thought waves could be put in the same state like photons yet electrons can not exist in the same state.
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3Please note that the wave nature of electrons, even the ones bound to atoms, is a probability wave, not a material/energy wave. That means that the mathematical functions that describe the probability of finding an electron in (x,y,z,t) are wave like. Usual waves are energy transfer waves, like sound or even electromagnetic waves in classical electrodynamics. – anna v Mar 23 '13 at 15:41
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Note: The probability wave is a Copenhagen Interpretation of wave functions. – user4884 Mar 29 '13 at 11:55
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Yes, but it is supported by experiment . Nothing mystical about it. – anna v Mar 29 '13 at 12:15
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Experimental results still have to be interpreted and this is where interpretations become mystical. Experiment also supports the fact that Schrodinger's equation is valid for all size wave functions. The statistical form for all amplitudes can be maintained without normalization but the Copenhagen Interpretation cannot prove it. I believe renormalization provides proof on the atomic level. – user4884 Mar 29 '13 at 12:55
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Electrons are a fundamentally different field than photons - don't expect them to obey exactly the same laws. The Pauli exclusion principle only governs the behaviour of fermions (e.g. electrons). Bosons (e.g. photons) are not bound by it (except for very special exceptions).
If you want to go down deeper (in other words you are curious why there is something like Pauli exclusion principle at all) read a bit about the spin-statistics theorem. It follows mostly from the requirement of particle undistinguishability.
peterph
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Electrons move in the same way that photons do. They are little disturbances of a quantum field, and the same general principles govern their motion as govern the long distance physics of any quantum field. (For example, the classical electron field satisfies a local differential equation, the Dirac equation.)
But electron waves behave differently from photon waves in that they are massive, so it's far more energetically expensive to create them. You can only have finitely many disturbances in the electron field with a given energy budget, whereas you can have arbitrarily many photons. Also, they are fermionic. The electron field is anticommutative; it's disturbances repel each other in a way that makes it impossible to pile them up.
Waffle's Crazy Peanut
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user1504
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[...] but I thought waves could be put in the same state like photons yet electrons can not exist in the same state.
I suspect that when you say "I thought waves could be put in the same state", you are thinking roughly of the superposition principle. Confounding this with the exclusion principle, which forbids two electrons from occupying the same quantum state, will result in confusion.
The smoking gun that reveals the wave aspect of the electron is the ability of a single electron to interfere with itself. In this context the exclusion principle is conceptually irrelevant because the phenomenon is exhibited by a single particle.
Joshua Barr
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No. Electron are not considered waves. Electrons are considered particles and studied in a branch of physics named particle physics. Everything is found to be made of particles. Waves (e.g. electromagnetic waves) are just collections of particles.
The myth that electrons are waves or behave as waves or sometimes are waves and sometimes are not, depending of the observer, is one of the more persistent myths that surround quantum mechanics.
Electrons can exist in the same state. E.g. one electron in an hydrogen atom can be in the same state than another electron in another atom. What happens here is that two electrons cannot be in the same state in the same atom at the same instant, because there is only one such state available in a single atom.
juanrga
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2This is not correct, as is shown by the two-slit experiment where individual particles give an interference pattern, a wave like property. This is not even to mention the clear probability-wave behavior of electrons observed in the orbitals of the hydrogen atom. – Tyberius Jul 05 '18 at 19:13
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@Tyberius The two-slit experiment prove that particles aren't waves. The observed wave-like pattern is a property of the ensemble not of individual particles. Check this answer https://physics.stackexchange.com/a/46303/12998 where you can see a time-resolved two-slit experiment instead only the final result of the experiment. Those points are particles impacting the screen. – juanrga Jul 06 '18 at 09:51
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I am not a genius as I am only 14 but I think I can answer this question, so I'll give it a shot.
If you have heard of the photoelectric effect, you can view electrons as particles. When high energy photons, individually hit electrons they get hyped up and break off the metallic bonding structure. However, the energy of the electron after it leaves depends only on the frequency of the light beam (Which is the energy of individual photons).
However, when the double-slit experiment was conducted with electrons these were the results.
This led to scientists thinking of electrons as waves as interference is visible.
Because they act like both waves and particles electrons are considered to be am example of "particle-wave duality", meaning that they are both particles and waves at every instant of time. Not only electrons or photons though, all matter, according to Prince de Brogile, can be thought of as both matter and waves. He used, roughly speaking, Einstein's E=mc^2 and Planck's E=hv and stated that since mass is a form of energy and all energy can be expressed as waves with specified wavelengths. So, not only electrons or photons but all matter, includding us and possibly the whole universe, can be expressed as one single wave with a specific wavelength.
Kush
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