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gametheory

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- Thread starter gametheory
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- #1

gametheory

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- #2

Faradave

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I'm just a beginner myself, so wait for other replies. I've found that if spin is measured along a given axis of a spin½ particle, then the probability (p) that spin then measured along another axis will have the same sign (+ or -) is:

p = cos(α)/2 + 50%,

where α is the angle the new axis makes with the original axis.

Good luck!

p = cos(α)/2 + 50%,

where α is the angle the new axis makes with the original axis.

Good luck!

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- #3

gametheory

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- #4

dipstik

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you want to look at stern-gerlach experiment i think. should be some good reading.

- #5

Bill_K

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- #6

Faradave

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That looks like it works. Do you know where this comes from?

I'm afraid I made mine up from a table of some spin correlations.

- #7

DrChinese

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Cos^2(theta/2) = Cos(theta)/2 + .5

Where theta = {0, 45, 60, 90 degrees} that looks pretty good.

- #8

Faradave

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Interesting! My daughter's old precalculus book lists the "Double Angle Formulas":

cos2θ = 2cos^{2}θ -1 = 1 - 2sin^{2}θ = cos^{2}θ - sin^{2}θ, also

sin2θ = 2sinθcosθ

This raised a follow-up question, if I may. (I'll start a new thread if needed.)

Over what range of angles is the quantum spin correlation formula considered complete?

The table I had listed five spin correlations from 0° to 180°. Classical trigonometry addresses 360° in its unit circle. But it seems that quantum spin is associated with a 720° rotation, at least for fermions.

cos2θ = 2cos

sin2θ = 2sinθcosθ

This raised a follow-up question, if I may. (I'll start a new thread if needed.)

Over what range of angles is the quantum spin correlation formula considered complete?

The table I had listed five spin correlations from 0° to 180°. Classical trigonometry addresses 360° in its unit circle. But it seems that quantum spin is associated with a 720° rotation, at least for fermions.

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