Pauli spin matrices: Difference between revisions
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The '''Pauli spin matrices''' (named after physicist [[Wolfgang Ernst Pauli]]) are a set of unitary [[Hermitian matrix|Hermitian matrices]] which form an orthogonal basis (along with the identity matrix) for the real [[Hilbert space]] of 2 × 2 Hermitian matrices and for the complex Hilbert spaces of all 2 × 2 matrices. They are usually denoted: | The '''Pauli spin matrices''' (named after physicist [[Wolfgang Ernst Pauli]]) are a set of unitary [[Hermitian matrix|Hermitian matrices]] which form an orthogonal basis (along with the [[identity matrix]]) for the real [[Hilbert space]] of 2 × 2 Hermitian matrices and for the complex Hilbert spaces of all 2 × 2 matrices. They are usually denoted: | ||
: <math>\sigma_x=\begin{pmatrix} | : <math>\sigma_x=\begin{pmatrix} |
Revision as of 17:40, 9 December 2008
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The Pauli spin matrices (named after physicist Wolfgang Ernst Pauli) are a set of unitary Hermitian matrices which form an orthogonal basis (along with the identity matrix) for the real Hilbert space of 2 × 2 Hermitian matrices and for the complex Hilbert spaces of all 2 × 2 matrices. They are usually denoted:
Algebraic properties
For i = 1, 2, 3:
Commutation relations
The Pauli matrices obey the following commutation and anticommutation relations:
- where is the Levi-Civita symbol, is the Kronecker delta, and I is the identity matrix.
The above two relations can be summarized as: