Simple derivation of Schrödinger equation from Newtonian dynamics Michele Marrocco Dipartimento di Fisica, Università di Roma ‘La Sapienza’ P.le Aldo Moro 5, I-00185 Rome, Italy & ENEA (Italian National Agency for New Technologies, Energies and Sustainable Economic Development) via Anguillarese 301, I-00123 Rome, Italy
A few years ago, one of the former Editors of this journal launched “a call to action” (E. F. Taylor, Am. J. Phys. 71, 423 (2003)) for a revision of teaching methods in physics in order to emphasize the importance of the principle of least action. In response, we suggest the use of Hamilton’s principle of stationary action to introduce the Schrödinger equation. When considering the geometric interpretation of Hamilton-Jacobi theory, the real part of the action 𝑆 defines the phase of the wave function 𝑒𝑥𝑝(𝑖𝑆/ℏ) and requiring the Hamilton-Jacobi wave function to obey wave-front propagation (i.e., Re(𝑆) is a constant of the motion) yields the Schrödinger equation…
