Describing the Restricted Qubit State is the best introduction I've seen on the Bloch sphere, but one thing still bugs me...
Question: Why use $θ/2$ instead of $θ$ or $zθ$ for that matter (i.e. ANY non-zero real factor of $θ$ will do)? Once we choose $\phi=0$ (so $e^(i\phi)=1$, making everything real), EVERY choice of $x$ for $\cos^2(x) + \sin^2(x)$ will normalize the probabilities (i.e. produce a $1$). There must be something else driving the choice of $θ/2$; what is it?
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4does Why are half angles used in the Bloch sphere representation of qubits? answer your question? – glS Mar 31 '22 at 08:52
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Still intuitively confusing, but I see how the 1/2 sneaks inside the trig functions. – DarkSky Apr 12 '22 at 10:34