A spin state of an electron in the vector form is given by 3i X = A (a) Determine the normalization constant A, assuming it to be real and positive. (b) Write down the X using the X+ and X-. If z-component of the spin of the electron is measured, what is the probability of finding the value in +ħ/2? (e) Determine the expectation value and uncertainty of S in terms of h when the electron is in spin state x. Justify your answer. (d) Determine the expectation value of the product S'S, in terms of h when the electron is in spin state X.

A spin state of an electron in the vector form is given by 3i X = A (a) Determine the normalization constant A, assuming it to be real and positive. (b) Write down the X using the X+ and X-. If z-component of the spin of the electron is measured, what is the probability of finding the value in +ħ/2? (e) Determine the expectation value and uncertainty of S in terms of h when the electron is in spin state x. Justify your answer. (d) Determine the expectation value of the product S'S, in terms of h when the electron is in spin state X.