Pauli vector

Noun

(mathematics) A vector whose components are Pauli matrices; e.g., ⃑𝜎=𝜎₁̂i+𝜎₂̂j+𝜎₃̂k.

Japanese Meaning

パウリ行列（パウリマトリックス）を各成分に持つベクトル。数学（特に量子力学）において、パウリ行列を用いたベクトル表現を意味する。

What is this buttons?

The Pauli vector provides a convenient representation of spin operators in three-dimensional space.

Google Translation / DeepL Translation

成分がパウリ行列であるベクトルは、三次元空間におけるスピン演算子を簡潔に表現するのに便利です。

Details

Sense（1）

(mathematics) A vector whose components are Pauli matrices; e.g., ⃑𝜎=𝜎₁̂i+𝜎₂̂j+𝜎₃̂k.

The eigenvectors of the first Pauli matrix "encode" — as it were — the +X and −X directions. Likewise, the eigenvectors of the second Pauli matrix "encode" the +Y and −Y directions and those of the third Pauli matrix, the +Z and −Z directions. The dot product of the Pauli vector with any unit vector ⃑N yields a matrix which likewise has eigenvalues +1 and −1 and a pair of eigenvectors; the eigenvector with positive eigenvalue "encodes" the +N direction and the eigenvector with negative eigenvalue "encodes" the −N direction. The dot product of any two such "encoded" directions yields the probability amplitude that the spin of an electron prepared in the first direction will collapse to the second direction when measured along that second direction.

Google Translation / DeepL Translation