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Is there a general method for an arbitrary value of S?

- Thread starter salsero
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- #1

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Is there a general method for an arbitrary value of S?

- #2

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If we rotate by an angle φ, then each spin 1/2 has a probability P(+)=[cos(φ/2)]^2 of having projection "up" along z, and a probability P(-)=[sin(φ/2)]^2 of being "down". For that whole system to have projection K (where |K|<=2J), then we will have J+K spins pointing up and J-K spins pointing down. The probability of this projection is expressed in terms of P(+) and P(-), such that

P(K)=(2J choose J+K)*P(+)^(J+K)*P(-)^(J-K)

where "2J choose J+K" is equal to (2J)!/[(J+K)!(J-K)!]

- #3

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Is this something you thought about now, or you read/learned this trick somewhere in the past?

- #4

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Actually, it was an assignment question a few weeks ago

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