Pauli exclusion principle, quantum states, and lasers?

[Juxtaroberto]

As I understand it, the Pauli exclusion principle states that no two like fermions can be in identical quantum states. I also understand that the quantum states are thus: $$n$$, which is the electron shell, $$l$$, which is the subshell, $$m_{l}$$, which is orbital, and $$m_{s}$$, which is spin. However, it seems that this explanation only talks about electrons in a single atom... that is, two electrons can both have the exact same quantum numbers as long as they are in two separate atoms. Am I missing something? Are there other quantum numbers, or something?

Also, I once heard it told that the fact that bosons do not obey the Pauli exclusion principle is the reason we can make lasers with them (well, with photons, which are bosons). Why does the Pauli exclusion principle prevent fermions into being in lasers, or some similar application? What is it about lasers that bosons can be in them, but not fermions?

And lastly, there are certain elements whose spin add up to integer values, and others whose spin add up to half integer values... does this literally mean that those with integer value can have identical quantum states, and those with half integer can't? Wouldn't the fact that the nucleons in the atoms are half-integer particles affect this?

 

[Juxtaroberto]

No, no one?

 

[Drakkith]

Two fermions cannot occupy the same place AND have the same quantum states. You could think of the position as a quantum state I suppose. Two electrons can occupy the same atomic orbital, but both have to have a different spin. Electrons in different atoms do not occupy the same spot since they are in different atoms.

A laser is a continuous "beam" made up of photons that are all in phase with each other and very close to the same wavelength. Lasers are formed by the stimulated emission of radiation inside a medium. You CANNOT have a laser that is formed out of anything but light. It wouldn't be a laser then. The pauli exclusion principle has nothing to do with not allowing other particles to be a laser, its simply a completely different thing to have a laser and to have a particle beam.

 

[Juxtaroberto]

So, unless I'm greatly misunderstanding, does that mean two bosons can be in the same place at the same time? What about composite bosons?

 

[_PJ_]

Bosons are entirely unaffected by the exclusion principle.

For photons to be in the same place at the same time, you can consider interference of their wave nature, but the "position of a wave" is nonsensical.

 

[A. Neumaier]

What is it about lasers that bosons can be in them, but not fermions?

Well lasers produce photons, by the way they are constructed, and photons are bosons.
Nobody would call an electron gun (which produces fermions) a laser...

And lastly, there are certain elements whose spin add up to integer values, and others whose spin add up to half integer values... does this literally mean that those with integer value can have identical quantum states, and those with half integer can't?

Yes. This happens in superconductors and superfluids; see, e.g., http://en.wikipedia.org/wiki/BCS_theory

 

[Juxtaroberto]

Thanks, you guys have been really helpful.

Although, let me rephrase that question... should photons cease to be bosons and become fermions, for whatever reason, is there anything in the nature of lasers that could go against the Pauli exclusion principle?

 

[Drakkith]

Thanks, you guys have been really helpful.

Although, let me rephrase that question... should photons cease to be bosons and become fermions, for whatever reason, is there anything in the nature of lasers that could go against the Pauli exclusion principle?

I don't believe so.

 

[A. Neumaier]

should photons cease to be bosons and become fermions, for whatever reason, is there anything in the nature of lasers that could go against the Pauli exclusion principle?

Any source producing a beam of Fermions will respect the Pauli exclusion principle.