Quantum-mechanics equations {Lagrange equations} relate positions and velocities. Lagrange equations depend on energy conservation. Potential-energy change plus kinetic-energy change equals zero. In one space dimension, m * D((d^2x/dt^2) * dx) / Dx + m * dv / dt = 0. Because they use acceleration, Lagrange equations are second-order differential equations. Lagrange equations have same form for all three (equivalent) spatial coordinates. Lagrange equations have same form in all transformed coordinate systems, because kinetic energy plus potential energy is constant for both old and new coordinate systems.
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Date Modified: 2022.0224