Action Principle and Hamilton–Jacobi Equation as Wavefront Dynamics
Abide by Reason revisits the classical action principle for viewers who know Newton’s (F=ma) but not the Hamilton–Jacobi formulation that Schrödinger used as his starting point.
Hamilton’s Optical–Mechanical Analogy and Action Wavefronts
This note is for learners who want to see how Hamilton unified rays and waves in optics and then carried that picture into mechanics.
Maxwell Wave Equation, Eikonal Limit, and Guidance from Optics
Abide by Reason revisits classical wave optics to show how Schrödinger’s search for a mechanical wave equation was guided by existing electromagnetic theory.
Schrödinger’s Variational Functional and Replacing Quantum Conditions
This note is for learners who want to see the key conceptual leap that turns Hamilton–Jacobi mechanics into wave mechanics in Schrödinger’s hands.
Derivation of the Time-Independent Schrödinger Equation from Variational Principle
Abide by Reason details how Schrödinger’s stationary functional (J[\psi]) leads to the familiar time-independent Schrödinger equation for bound states.