Kets (state vectors). Consider the following three (candidate) state vectors: |4₁) = 3| +) − 4 |−) |4₂) = 2| +) + i|−) -in |3) = | +)-2 e|-) a) [1] Normalize each of the above states (following our convention that the coefficient of the | +) basis ket is always positive and real.) b) [1] 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!
Kets (state vectors). Consider the following three (candidate) state vectors: |4₁) = 3| +) − 4 |−) |4₂) = 2| +) + i|−) -in |3) = | +)-2 e|-) a) [1] Normalize each of the above states (following our convention that the coefficient of the | +) basis ket is always positive and real.) b) [1] 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!
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I need some help with this quantum physics problem.
![Kets (state vectors). Consider the following three (candidate) state vectors:
14/1)
|4₁) = 3| +) − 4 |-)
-
1/₂) = 2| +) + i|-)
-in
|43) = | +) − 2 e¯47² | −)
a) [1] Normalize each of the above states (following our convention that the coefficient of the
| +) basis ket is always positive and real.)
b) [1] 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) [1] For JUST the second state, [₂), find the probability that the spin component will be “up”
along the X-direction. Use bra-ket notation in your calculations.
d) [2] For JUST state 3), 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 nasty complex-
number arithmetic required on this one that is very important, and people frequently make
mistakes on it that change the answer significantly!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b00a09c-5597-457d-8151-edd0c392eea7%2Ff568def1-e013-4ba2-9a7a-a04ea31241f6%2Fcj3nl2g_processed.png&w=3840&q=75)
Transcribed Image Text:Kets (state vectors). Consider the following three (candidate) state vectors:
14/1)
|4₁) = 3| +) − 4 |-)
-
1/₂) = 2| +) + i|-)
-in
|43) = | +) − 2 e¯47² | −)
a) [1] Normalize each of the above states (following our convention that the coefficient of the
| +) basis ket is always positive and real.)
b) [1] 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) [1] For JUST the second state, [₂), find the probability that the spin component will be “up”
along the X-direction. Use bra-ket notation in your calculations.
d) [2] For JUST state 3), 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 nasty complex-
number arithmetic required on this one that is very important, and people frequently make
mistakes on it that change the answer significantly!
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