3. An electron is in a spin state, whose wavefunction in the S eigenbasis is A...

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3. An electron is in a spin state, whose wavefunction in the S₂ eigenbasis is A (²+1) 2i a. Calculate the normalization factor A? b. If we measure S₂ on this electron, what values will you get and what are their corresponding probability? Also calculate the expectation value and uncertainty for the S₂ operator. c. Answer the same questions as in part b for Sx and Sy respectively. d. Show that the uncertainty product of Sx and Sy satisfies the generalized uncertainty principle. 3. An electron is in a spin state, whose wavefunction in the S₂ eigenbasis is A (²+1) 2i a. Calculate the normalization factor A? b. If we measure S₂ on this electron, what values will you get and what are their corresponding probability? Also calculate the expectation value and uncertainty for the S₂ operator. c. Answer the same questions as in part b for Sx and Sy respectively. d. Show that the uncertainty product of Sx and Sy satisfies the generalized uncertainty principle.