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Higgsono
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What is the explanation for the case that fermion's can't occupy the same quantum state? Is there some logic behind this or is it just observation?
Do you have any reference for this statement? Does it mean that having two electrons, one with ##l=0,m_l=0,m_s=1/2## and the other ##l=2,m_l=2,m_s=1/2## (so ##L=2##, ##S=1##) is not allowed?mikeyork said:UAn alternative expression of the rule (and one that relates directly to observables) is that L+S must be even in the CM frame (equal and opposite momentum) for any pair of identical particles, where L is the net orbital angular momentum and S is the net spin angular momentum.
Good question! The L+S rule comes from SU(2) couplings given the usual anti-symmetry. Off the top of my head I think the answer to your question is that you can't get those two specific orbital states in the CM frame because of the spatial symmetry relating the angular co-ordinates (their momenta point in opposite directions). So, for instance you could have l1 = l2 = 1 and then the L=1 state would require s1 = s2. From memory I think the original rule comes from the classic Jacob & Wick* paper on helicity states, but you can also find it in my spin-statistics papers (which I haven't linked because they are not accepted mainstream for other reasons). PM me if you want further information.DrClaude said:Do you have any reference for this statement? Does it mean that having two electrons, one with ##l=0,m_l=0,m_s=1/2## and the other ##l=2,m_l=2,m_s=1/2## (so ##L=2##, ##S=1##) is not allowed?
The Pauli Exclusion Principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This means that in a system, each fermion must have a unique set of quantum numbers.
The Pauli Exclusion Principle was first proposed by Austrian physicist Wolfgang Pauli in 1925. It was later refined by Enrico Fermi in 1926.
The Pauli Exclusion Principle is significant because it explains many important properties of matter, such as the periodic table of elements and the stability of atoms. It also plays a crucial role in understanding the behavior of electrons in atoms and molecules.
No, the Pauli Exclusion Principle is a fundamental law of nature and has been experimentally verified numerous times. It is not possible for fermions to violate this principle.
Electrons, as fermions, must follow the Pauli Exclusion Principle. This means that in an atom, each electron occupies a unique quantum state, and no two electrons can share the same set of quantum numbers. This principle also explains the arrangement of electrons in different energy levels and orbitals within an atom.