I started a thread "Quantum Mechanics Basics" a while ago, but the demand seemed to decline (that was at ~1k followers) I'd be happy to start it back up if you'd all likehttps://twitter.com/InertialObservr/status/1087087279670095872 …
PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …
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〈 Berger | Dillon 〉 Retweeted 〈 Berger | Dillon 〉
I started a thread "Quantum Mechanics Basics" a while ago, but the demand seemed to decline (that was at ~1k followers) I'd be happy to start it back up if you'd all likehttps://twitter.com/InertialObservr/status/1087087279670095872 …
〈 Berger | Dillon 〉 added,
Isn't the dot product already the squared magnitude?pic.twitter.com/1briCwprrz
hmm no for instance a*b can be negative or positive |a*b|^2 is real positive definite
Ah, so |𝜙⟩ and |-𝜙⟩ are indistinguishable. Reminds me of quaternion double cover of 3D orientations. Square root of scaling factor makes sense there, since you need sandwich product to apply rotation which has side effect of applying any scaling twice.
Actually, for normalized states |𝜙⟩ and Exp(i θ) |𝜙⟩ are indistinguishable for any phase θ. These equivalence classes are often called rays, and the space of such rays correspond to the space of pure quantum states. This is very similar to Projective spaces.
That’s right
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