Kets (state vectors). Consider the following three (candidate) state vectors: 142) = 3] +) - 41-) 142) = 2] +) + il-) 143) = 1 +) – 2e751-) a) Normalize each of the above states (following our convention that the coefficient of the 1+> basis ket is always positive and real.)
b) For each of these three states, find the probability that the spin component will be "up" along the Z-direction. Use bra-ket notation in your calculations!
c) For JUST the second state, 142), find the probability that the spin component will be "up" along the X-direction. Use bra-ket notation in your calculations. (Hint: you will need McIntyre eq 1.36 for this one. You will need McIntyre 1.60 for the next part!)
d) For JUST state [43), find the probability that the spin component will be "up" along the Y-direction.
Use bra-ket notation in your calculations. Be careful, there is some slightly nasty complex-number arithmetic required on this one that is very important, and frequently people make mistakes on it that turn out to really change the answer significantly!