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davelee
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Pauli's exclusion principle states that no two fermions may occupy the same quantum state. But why is this so? Is there a "why" explanation, as opposed to merely saying that this is the way it is?
Originally posted by futz
It has to do with the fact that for fermions, the wavefunction for two particles must be antisymmetric.
Originally posted by suyver
However, I think that this is an assumption and not something that one can prove from quantum mechanics.
Originally posted by futz
However, the PEP (and for that matter, spin itself) is a direct consequence of relativistic QM, and falls naturally out of the theory. [/B]
Originally posted by jefferywinkler
Consequently, the wavefunction must vanish if the two fermions are located in the same state. Only 0 or 1 fermion can be there in one state, and this fact is essential for chemistry to work, for example, because we need the electrons to fill the different shells.
Originally posted by jeff
Well, the exclusion principle explains the existence of atomic orbital structure,
Originally posted by Tom
You can solve the Schrodinger equation and determine the atomic orbital structure without ever encountering the exclusion principle. The PEP does not determine the orbitals, it determines how the orbitals are populated.
Originally posted by jeff
I meant that without the PEP, there would be no orbital structure at all - whatever it's properties - since the orbit of electrons about atomic nuclei would decay. Thus rather than "existence of the observed..." I should've said "the observed existence...".
Originally posted by lethe
...the exclusion principle does not affect the solutions to the Schrödinger equation...
Originally posted by lethe
...without the exclusion principle, the ground state of an atom would have all electrons in the lowest orbital.
Originally posted by jeff
Without the exclusion principle, orbits of negatively charged electrons about positively charged atomic nuclei would rapidly decay with the electrons plunging directly into nuclei and ending up sharing the same state. The PEP forbids such degeneracies.
Originally posted by lethe
i don t believe this. are you sure? if i found a selectron, let's suppose its stable and has the same mass and charge as the electron, only its a boson, could i not put it in the 1s orbital around a proton? what would cause it to spiral in?
doesn t this system still follow Schrödinger's equation? doesn't Schrödinger's equation have a lowest energy level solution for the hydrogen atom? the particle cannot go to a lower en energy level, completely independently of whether the particle is a boson or a fermion, it seems to me.
am i missing something here?
or, look at it another way, the bosons obey the Heisenberg Uncertainty Principle, right? so they plunge into the nucleus, but they can t stay there, and they won't be anihilated, so they come out again.
in fact, this is the same layman's argument for how Quantum Mechanics restored the stability of the unstable classical atom. i don t see how the fermionic or bosonic nature of the electron has any bearing on this argument.
Originally posted by jeff
Oh well, happy new year.
Pauli's exclusion principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that in a given atom or molecule, each electron must have a unique set of quantum numbers, including its energy level, orbital, and spin.
Pauli's exclusion principle is a fundamental principle in chemistry because it explains the stability of atoms and the periodic table. Without this principle, all electrons would be able to occupy the lowest energy levels, leading to unstable atoms and molecules. The exclusion principle also explains chemical bonding and the formation of chemical compounds.
The Heisenberg uncertainty principle states that the position and momentum of a particle cannot be known simultaneously with absolute precision. This principle also applies to electrons, meaning that their exact energy levels cannot be determined. Pauli's exclusion principle then comes into play by limiting the number of electrons that can occupy a particular energy level, thus reducing the uncertainty in the system.
Yes, there are a few exceptions to Pauli's exclusion principle. One exception is in the case of degenerate energy levels, where two or more electrons can occupy the same quantum state if they have different spins. Another exception is in nuclear physics, where the principle applies to nucleons (protons and neutrons) in a nucleus, rather than electrons in an atom.
Pauli's exclusion principle was first proposed by Austrian physicist Wolfgang Pauli in 1925. He came up with the idea while trying to explain the structure of atoms and the periodic table. The principle was later confirmed by experiments and has since become a fundamental concept in quantum mechanics and chemistry.