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03 Classical Wave

In this video, I work through the separation of variables approach to solving the one-dimensional classical wave equation. We focus specifically on the case where the separation variable k is negative, and show how applying boundary conditions leads to physically meaningful standing-wave solutions. This lecture is intended as preparation for Quantum Mechanics, where the same mathematical structure appears in the Schrödinger equation. Emphasis is placed on: Setting up the separation of variables Interpreting the separation constant Solving the spatial and temporal equations Applying boundary conditions Understanding the physical meaning of the resulting modes This walkthrough is especially useful for students transitioning from classical PDEs to quantum systems such as the particle in a box.