DIRECTION: Please provide a step-by-step and clear solution to each of the problems below. 3) The three Pauli spin matrices are 0x = (₁₁₂2)₁ ²₂ = %₂ = (i (₁ ²), and °₂ = (1 91₁). Show that (a) (0₂)² = (0₂)² = (0₂)² = 12, where 1₂ = (19) the 2 x 2 identity matrix. (b) σxσy = iσ₂, 0₂0₂ = iσx, and σ₂0x = iσy.
DIRECTION: Please provide a step-by-step and clear solution to each of the problems below. 3) The three Pauli spin matrices are 0x = (₁₁₂2)₁ ²₂ = %₂ = (i (₁ ²), and °₂ = (1 91₁). Show that (a) (0₂)² = (0₂)² = (0₂)² = 12, where 1₂ = (19) the 2 x 2 identity matrix. (b) σxσy = iσ₂, 0₂0₂ = iσx, and σ₂0x = iσy.
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Transcribed Image Text:DIRECTION: Please provide a step-by-step and clear solution to each of the problems below.
3) The three Pauli spin matrices are
0x
= (₁ ₂), ₁₂ = (i 3),
and oz
= (1 9₁₂).
Show that
(a) (0₂)² = (0₂)² = (0₂)² = 12, where 1₂ = (19) the 2 x 2 identity matrix.
(b) 0x0y = iσ₂, 0₂0₂ = 10x, and
=
070x
ioy.
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