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In this video, I use the inner product and some even/odd symmetry properties stolen from physical chemistry to derive the governing differential equations when you apply light to a two-level system. The resultant equations can actually be solved with known initial conditions, and that solution is Fermi's Golden Rule.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
