Pauli matrix

English

Etymology

Named after Template:W (1900–1958), Austrian theoretical physicist.

Noun

1. Template:Lb Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics.

   The Pauli matrices satisfy the equation ${\sigma }_1^2={\sigma }_2^2={\sigma }_3^2=-i{\sigma }_1{\sigma }_2{\sigma }_3=I$ which is reminiscent of Hamilton's fundamental formula for quaternion multiplication.

   The first Pauli matrix is like a reflection about the "y=x" line. The third Pauli matrix is like a reflection about the "x axis". The second Pauli matrix is like a 90° counterclockwise rotation and scalar multiplication by the imaginary unit (which rotates the two complex components by 90° counterclockwise in their own "phasor spaces", as it were).

   The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. —Template:W

Hypernyms

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Holonyms

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