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## Main Question or Discussion Point

I know the principle says that no two fermions canNot have the same atomic number, but could you explain that in detail?

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I know the principle says that no two fermions canNot have the same atomic number, but could you explain that in detail?

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Ken G

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tom.stoer

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Are you familiar with the harmonic oscillator?I know the principle says that no two fermions canNot have the same atomic number, but could you explain that in detail?

Fermionic creation and annihilation operators are constructed using anti-commutators (instead of commutators

[tex]\{b_s,b^\dagger_{s^\prime}\} = \delta_{s\,s^\prime}[/tex]

[tex]\{b_s,b_{s^\prime}\} = \{b^\dagger_s,b^\dagger_{s^\prime}\} = 0[/tex]

The last equation is important b/c for s=s' it can be rewritten as :

[tex](b^\dagger_s)^2 = 0[/tex]

s,s' represent the quantum numbers

You can construct a states where each s, s', s'', ... is occupied by either zero or one particle. But if you want to construct a state with two particles sitting in state s you get

[tex]|2s\rangle = (b^\dagger_s)^2|0\rangle = 0[/tex]

due to the anticommutator.

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They can be in the same state as long as they have different positions though right?

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tom.stoer

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Sorry, I forgot to explain that creation and annihilation operators act in momentum space and that this means that s is a collection of momentum, spin, isospin, etc.}. Therefore they are not located anywhere in position space.They can be in the same state as long as they have different positions though right?

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