What makes lasers so special: Lasers vs other light sources.
How Lasers Work by Scientized (2017)
Source. An extremely good overview of how lasers work. Clearly explains the electron/photon exchange processes involved, notably spontaneous emission.
Talks about the importance of the metastable state to achieve population inversion.
Also briefly explains the imperfections that lead to the slightly imperfect non punctual spectrum seen in a real laser.
- youtu.be/_JOchLyNO_w?t=188 says LED is "also monochromatic", but that is not strictly true, it has way way larger frequency band than a laser. Only narrower compared to other sources such as incandescent light bulbs.
- youtu.be/_JOchLyNO_w?t=517 stimulated emission. This is the key to laser formation as it produces coherent photons.
- youtu.be/_JOchLyNO_w?t=581 spontaneous emission happens too fast (100 ns), which is not enough time for stimulated emission to happen. Metastable electrons to the rescue.
- youtu.be/_JOchLyNO_w?t=832 the parallel mirrors select perpendicular photons preferentially
The wave equation can be seen as infinitely many infinitesimal coupled oscillators Updated 2025-05-21 +Created 1970-01-01
TODO confirm, see also: coupled oscillators. And then this idea can be used to define/motivate quantum field theory in terms of quantum harmonic oscillators with second quantization.
- youtu.be/SMmFgIEGYtw?t=324 Quantum Field Theory 2a - Field Quantization I by ViaScience (2018)
Chapter 2 paragraph 14:
Formerly, I, Zhuang Zhou, dreamt that I was a butterfly, a butterfly flying about, feeling that it was enjoying itself. I did not know that it was Zhou. Suddenly I awoke, and was myself again, the veritable Zhou. I did not know whether it had formerly been Zhou dreaming that he was a butterfly, or it was now a butterfly dreaming that it was Zhou. But between Zhou and a butterfly there must be a difference. This is a case of what is called the Transformation of Things.'
Fundamental question related to Ciro's 2D reinforcement learning games.
Bibliography:
- youtu.be/i0UyKsAEaNI?t=120 How to Build AGI? Ilya Sutskever interview by Lex Fridman (2020)
Started at Google Quantum AI in 2014.
Has his LaTeX notes at: github.com/DanielSank/theory. One day he will convert to OurBigBook.com. Interesting to see that he is able to continue his notes despite being at Google.
Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.
But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.
One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.
How To Get Tenure at a Major Research University by Sean Carroll (2011) Updated 2025-05-21 +Created 1970-01-01
We define this as the functional equation:It is a bit like cauchy's functional equation but with multiplication instead of addition.
There are unlisted articles, also show them or only show them.