3. The Pauli matrices are defined as %3! Here, i is the complex number satisfying i? = -1. Prove each of the following statements: %3D (a) o= o = o? = -io,0,0; = 0 ) (= 1 or I, the identity matrix) %3D %3! (b) o,0, = io, %3D (c) o,T; – T;0y = 2io, %3!
3. The Pauli matrices are defined as %3! Here, i is the complex number satisfying i? = -1. Prove each of the following statements: %3D (a) o= o = o? = -io,0,0; = 0 ) (= 1 or I, the identity matrix) %3D %3! (b) o,0, = io, %3D (c) o,T; – T;0y = 2io, %3!
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Transcribed Image Text:3. The Pauli matrices are defined as
Here, i is the complex number satisfying i? = -1. Prove each of the following statements:
(a) o= o = o? = -io,o,o; = (=1 or I, the identity matrix)
%3D
(b) oơy = iơ,
(c) Tyo; - 020y = 2iox
!!
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