/ edmundsj
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In this video I explain what it means for two functions to be 'orthogonal', and how we test for this orthogonality. This is actually an absurdly useful property that allows us to greatly simplify the Schrodinger Equation before trying to solve anything. I would argue it is one of the most fundamental mathematical properties of functions (at least of use to engineers and physicists), and underlies things like the Taylor Series and Fourier Transforms.
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.