The math of superposition and quantum states.
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Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way.

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    • Essence of linear algebra  

Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18. Thanks for the catch!

*Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin.

What's the difference? Well, using a double-headed 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 single-headed notation throughout, though this runs slightly against convention.

Music by Vincent Rubinetti:
https://vincerubinetti.bandcamp.com/a...

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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