# xstate - z basis states | ± x = a | ± b |-± where a and...

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Physics 225/315 January 16, 2008 x and y basis states for Spin 1 2 Using SG devices prepare the states | + ± x and |-± x . Select the state | + ± x and measure | + ± and |-± with a SGz device. What is the probability of observing the output in the + z direction? The probability amplitude is ² + | + ± x . The probability or amplitude squared is + | + ± x | 2 . We observe a probability of 1/2. Write | + ± x as a linear combination of orthonormal
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Unformatted text preview: z basis states: | + ± x = a | + ± + b |-± where a and b are in general complex. Then we see that ² + | + ± x = a and we require | a | 2 = 1 2 to agree with the experiment. so we ﬁnd a = 1 √ 2 e iα . We will choose (by convention) α = 0 so a = 1 √ 2 . Similarly for b . So we ﬁnd that | + ± x = 1 √ 2 ( | + ± + |-± ) 1...
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