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The Mathematical Methods in Physical Science

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The Pauli spin matrices in quantum mechanics are

sigma_x = 0 1 sigma_y = 0 -i sigma_z = 1 0
1 0 i 0 0 -1

a) Show that (sigma_x)^2 = (sigma_y)^2 = (sigma_z)^2 = I (identity of unit matrix)

b) Show that (sigma_x)(sigma_y) - (sigma_y)(sigma_x) = 2i*sigma_z

c) Show that (sigma_x), (sigma_y) and (sigma_z) are Hermitian.

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