Some light quantum mechanics (with MinutePhysics)
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by Super User, 8 months ago
Learn more through active problemsolving at Brilliant: https://brilliant.org/3b1b
This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves.
I will say, if you *do* want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at http://3b1b.co/essenceoflinearalgebra
*Note on conventions: Throughout this video, I use a singleheaded right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use doubleheaded arrows for describing polarization states, while singleheaded arrows are typically reserved for the context of spin.
What's the difference? Well, using a doubleheaded arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there's no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you're in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state.
Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the singleheaded notation throughout, though this runs slightly against convention.
Special thanks to these patrons: http://3b1b.co/lightquantumthanks
Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/onetwozeta

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8 months ago