Question

Problem 8.4.16. (Very Important). Say hello to the Pauli matrices (8.4.45) 2 which you will see on numerous occasions. (The subscripts 1, 2, and 3 are some- tines used instead of x. У, and z.) Show that they are hermitian. Show that their square equals the unit matrix. Show that as a result of these two features they must also be unitary. Verify explicitly. Show that (8.4.46) Show that any two of them anticommute, i.e., the anticommutator (8.4.47) vanishes. Show that as a result (8.4.48) Find the determinants and the inverses of the three matrices by any method you want. Ifyou can avoid a calculation, that is fine.

Answer 1

Given data e mitan mti am 2. dC unit ratix

A matix kas called umitary as AA, Init MaHz.t」 Now Id un: ld

6队 2 enca Pvo ved yom

O -I 1 0 wo of he anticommute. уст HecPoved

Meleed Add aboe bwe Stalemet ļa.al, t la.ราะ(ns*5Ajt( a5-gn) from AV 7 2

der (rr) 2- 2. 2 2