Can someone help me to fully understand the Pauli Exclusion Principle?

Question

I believe this reflects my ignorance into what is exactly meant by a particle's quantum state? The principle states that no two fermions can occupy the same quantum state. Does that mean that no two fermions can co-exist in the same exact spot or is there maybe a quantum field existing between the electrons orbital and atom nucleus, and this whole field the area in which these two fermions cannot co-exist?

Answer 1

Yes, no two particles can occupy the same quantum state. Fermions are nothing more than a grouping of particles with spin 1/2. They cannot co-exist in the exact same quantum state. If more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin, or quantum state) must be different from the rest. So in order to have electrons in the lowest orbits, you have to have them in opposite spin pairs to fit properly.



I don't know if you are up to the level of Cohen-Tannoudji quantum mechanics, spin rotation operators, eigenvalues, eigen operators, anti-symmetric wave functions, etc, but it is a complicated, and rigorous demonstration that in order for things to work as they do, this exclusion principle must be correct.



Hope this helps...

Answer 2

Two fermions cannot exist in the same space interval at the same time.



But bosons can.



Fermions have spin 1/2 or -1/2. When two electrons are in the same orbital, one must have spin 1/2 and the other must have spin -1/2. This number represents the angular momentum of the electron.



Under certain conditions though, electrons can be forced together causing the Pauli Exclusion Principal to collapse.

Answer 3

This is normally a two hour lecture but I'll try to condense.



First of all the quatum state is defined as the mathematical construct that defines a quantum system. This would include the mass, velocity, position and energy level of all of the particles that make up the quantum system.



The Pauli Exclusion Principle applies to all particles of half-integer spin. This category includes all fundamental particles that make up what we normally think of as matter (protons, electrons, quarks, etc.) and it excludes all particles that mediate forces (photons, gluons, etc).



Briefly the principle states that no two electrons (having the same spin) can occupy the same energy level in an atom. As an analogy, think of the sun as the atomic nucleus. The planets are the electrons (they dont actually revolve around the nucleus but the orbit is analagous to an enery level in the atom). Now imagine that each "orbit" can only contain one "planet" or electron.



Now we could put another "planet" in that orbit if it had a different spin. Think of the earth as being a half-spin in an equatorial orbit around the sun. If you had a integer spin "planet" it might be analagous to being in a solar polar orbit.



Very simply put, you can't put two (indentical) things in the same place. Probably an even simpler view would be to think of an atom as having a wall full of slots, one for each location than an electron can occupy and each slot can only hold one.

Answer 4

"Quantum State" is not the same as "exact spot." Quantum particles don't have "exact spots" in which they are located. They have wave functions, probability distributions of position and momentum. The wavefunction is the same thing as "quantum state." No two identical fermions can exist with the same wavefunction.