Complex Numbers in Fourier Series and Quantum Mechanics

Explore complex numbers in Fourier Series and Quantum Mechanics through this 33-minute video from the "Classical to Quantum" playlist. Delve into Harmonic Analysis on Circles and Spheres using a rational algebraic approach, eschewing real numbers, transcendental functions, and infinite processes. Discover how complex numbers simplify elementary harmonic analysis on the unit circle, with a focus on the Laplacian operator and harmonic polynomials (polynumbers). Learn how this approach revolutionizes integration theory on circles, spheres, and hyperbolas, opening new avenues for pure mathematics and theoretical physics research.