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Derive Heisenberg's Uncertainty Principle in Quantum Mechanics in this 36-minute video featuring University of Oxford Mathematician Dr Tom Crawford and @MichaelPennMath. Begin with Schrödinger's Equation for the quantum wave function, solve for the time-dependent component, and explore the Stationary State Schrödinger Equation. Learn about momentum and position operators, expectation and dispersion of operators, and compute the commutator of position and momentum operators. Understand the key proposition used to derive Heisenberg's Uncertainty Principle and its proof using the positivity of a quadratic function. Conclude with the final formulation of the principle, demonstrating the relationship between the errors in measuring position and momentum. This video is part of a short series, following a previous lecture on Lie Algebras.
