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Show that the S² operator commutes with each of the spin component operators of S., S., and S₂. Do this once with matrix notation for a spin-1/2 system and a second time using only the component commutation relations in Eqs. (2.96) and the definition of S² in Eq. (2.103).

Show that the S² operator commutes with each of the spin component operators of S., S., and S₂. Do this once with matrix notation for a spin-1/2 system and a second time using only the component commutation relations in Eqs. (2.96) and the definition of S² in Eq. (2.103).

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Equation 2.96:

[Sx, Sy] = iħ(Sz)

[Sy, Sz] = iħ(Sx)

[Sz, Sx] = iħ(Sy)

Equation 2.103: S2 =  S2x + S2y + S2z 

Show that the S² operator commutes with each of the spin component operators of S., S., and S₂. Do this once with matrix notation for a spin-1/2 system and a second time using only the component commutation relations in Eqs. (2.96) and the definition of S² in Eq. (2.103). + n (Y) ? ? FIGURE 2.14 Measurement of spin components (Prob. 2.8). P. +y P-Y
Transcribed Image Text:Show that the S² operator commutes with each of the spin component operators of S., S., and S₂. Do this once with matrix notation for a spin-1/2 system and a second time using only the component commutation relations in Eqs. (2.96) and the definition of S² in Eq. (2.103). + n (Y) ? ? FIGURE 2.14 Measurement of spin components (Prob. 2.8). P. +y P-Y
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