# Pauli exclusion principle

• wolfgang pauli formulated the law stating that no two electrons can have the same set of quantum numbers.
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the pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously. this principle was formulated by austrian physicist wolfgang pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

in the case of electrons in atoms, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number, , the azimuthal quantum number, m, the magnetic quantum number, and ms, the spin quantum number. for example, if two electrons reside in the same orbital, then their n, , and m values are the same, therefore their ms must be different, and thus the electrons must have opposite half-integer spin projections of 1/2 and −1/2.

particles with an integer spin, or bosons, are not subject to the pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser or atoms in a bose–einstein condensate. this is because the exchange interaction, which relates the probabilities of two similar particles entering the same state, adds the probabilities together for bosons, instead being subtracted (and thereby cancelled out) as they are for fermions.

a more rigorous statement is that concerning the exchange of two identical particles the total wave function is antisymmetric for fermions, and symmetric for bosons. this means that if the space and spin coordinates of two identical particles are interchanged, then the wave function changes its sign for fermions and does not change for bosons.

• overview
• history
• connection to quantum state symmetry
• consequences
• see also
• references