2. Kets (state vectors). Consider the following three (candidate) state vectors: a) = 3|+) – 4|-) 42) = 2| +) + i|-) W3) = | +) – 2 e |-) a) Normalize each of the above states (following our convention that the coefficient of t +> 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, lV2), find the probability that the spin component will be "u along the X-direction. Use bra-ket notation in your calculations. (Hint: you will need Mclntyre eq 1.36 for this one. You will need Mclntyre 1.60 for the next part!)

2. Kets (state vectors). Consider the following three (candidate) state vectors: a) = 3|+) – 4|-) 42) = 2| +) + i|-) W3) = | +) – 2 e |-) a) Normalize each of the above states (following our convention that the coefficient of t +> 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, lV2), find the probability that the spin component will be "u along the X-direction. Use bra-ket notation in your calculations. (Hint: you will need Mclntyre eq 1.36 for this one. You will need Mclntyre 1.60 for the next part!)