Phase Space Trajectories and Conservation of Energy

The motivation for the derivation of the Schroedinger equation arising from the Law of Conservation of Energy as seen in the blog entry of December 13, 2022, is made clearer when one looks at the phase space trajectories in familiar classical settings. In the paper, Phase Space Curves and Conservation of Energy, we go through a few examples of how Newton's 2nd Law of motion and the conservation of energy are closely related and how the phase space trajectory gives insight into the equation that defines motion in quantum settings.