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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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Please 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
    
Note: The probability wave is a Copenhagen Interpretation of wave functions. –  user4884 Mar 29 '13 at 11:55
    
Yes, but it is supported by experiment . Nothing mystical about it. –  anna v Mar 29 '13 at 12:15
    
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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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.

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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.

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Check answer update or this nice discussion –  peterph Mar 25 '13 at 20:52

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.

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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.

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