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- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/05%3A_Interlude_-_The_Nature_of_Electrons/5.01%3A_Bosons_and_FermionsSo far, we have used Schrödinger’s equation to see how a single particle, usually an electron, behaves in a variety of potentials. If we are going to think about atoms other than hydrogen, it is neces...So far, we have used Schrödinger’s equation to see how a single particle, usually an electron, behaves in a variety of potentials. If we are going to think about atoms other than hydrogen, it is necessary to extend the Schrödinger equation so that it describes more than one particle. All elementary particles are either fermions, which have antisymmetric multiparticle wavefunctions, or bosons, which have symmetric wave functions. Electrons, protons and neutrons are fermions; photons are bosons.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/05%3A_The_Schrodinger_Equation/5.03%3A_The_Pauli_Exclusion_PrincipleAlthough all of the particles would love to occupy the lowest energy state, the Pauli Exclusion Principle states that no two identical fermions can occupy the exact same quantum state. Thus, only two ...Although all of the particles would love to occupy the lowest energy state, the Pauli Exclusion Principle states that no two identical fermions can occupy the exact same quantum state. Thus, only two neutrons (and two protons) can occupy the lowest energy state, one with spin “up” and one with spin “down”. In this way, the well is filled from the bottom up as indicted below:
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/04%3A_Identical_Particles/4.02%3A_Symmetric_and_Antisymmetric_StatesHence, Equation (???) is explicitly symmetric: \[\begin{align} \begin{aligned} \hat{P}_{12} \, |+\!z, A\,;\, -z, B\rangle &= \frac{1}{\sqrt{2}} \Big(|\!-\!z\rangle|B\rangle |\!+\!z\rangle|...Hence, Equation (???) is explicitly symmetric: ˆP12|+z,A;−z,B⟩=1√2(|−z⟩|B⟩|+z⟩|A⟩+|+z⟩|A⟩|−z⟩|B⟩)=|+z,A;−z,B⟩. Likewise, if there is a spin-down particle at A and a spin-up particle at B, the bosonic two-particle state is \[|-\!z, A\,;\, +z, B\rangle = \frac{1}{\sqrt{2}} \Big…
- https://phys.libretexts.org/Bookshelves/Modern_Physics/Spiral_Modern_Physics_(D'Alessandris)/6%3A_The_Schrodinger_Equation/6.3%3A_The_Pauli_Exclusion_PrincipleAlthough all of the particles would love to occupy the lowest energy state, the Pauli Exclusion Principle states that no two identical fermions can occupy the exact same quantum state. Thus, only two ...Although all of the particles would love to occupy the lowest energy state, the Pauli Exclusion Principle states that no two identical fermions can occupy the exact same quantum state. Thus, only two neutrons (and two protons) can occupy the lowest energy state, one with spin “up” and one with spin “down”. In this way, the well is filled from the bottom up as indicted below:
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/30%3A_Atomic_Physics/30.09%3A_The_Pauli_Exclusion_PrincipleThe state of a system is completely described by a complete set of quantum numbers. This set is written as (n, l, ml, ms). The Pauli exclusion principle says that no two electrons can have the same se...The state of a system is completely described by a complete set of quantum numbers. This set is written as (n, l, ml, ms). The Pauli exclusion principle says that no two electrons can have the same set of quantum numbers; that is, no two electrons can be in the same state. This exclusion limits the number of electrons in atomic shells and subshells. Each value of n corresponds to a shell, and each value of l corresponds to a subshell.
