Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three $2 \times 2$ complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter sigma ( $σ$ ), they are occasionally denoted by tau ( $τ$ ) when used in connection with isospin symmetries. They are

These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.

Each Pauli matrix is Hermitian, and together with the identity matrix $I$ (sometimes considered as the zeroth Pauli matrix $σ 0$ ), the Pauli matrices (multiplied by real coefficients) form a basis for the vector space of $2 \times 2$ Hermitian matrices.

Hermitian operators represent observables, so the Pauli matrices span the space of observables of the $2$ -dimensional complex Hilbert space. In the context of Pauli's work, $σ k$ represents the observable corresponding to spin along the $k$ th coordinate axis in three-dimensional Euclidean space $ℝ 3$ .

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