The famous uncertainty relation between position and momentum then follows directly from the canonical commutation relation [x,p] = iℏpic.twitter.com/7xTJdXHsNs
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The Generalized Heisenberg Uncertainty Relation
Two observables A & B can be measured simultaneously only if their corresponding operators commutepic.twitter.com/VY6LtptChv
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What’s the relationship between this and the fact that 2 matrices can be simultaneously diagonalized iff they commute?
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It means that the two operators cant be expanded in a common eigenbasis, and so don't have simultaneous observables
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As an exercise to demonstrate this I recommend the {train vs. light flash} It makes it very very clear.
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