A few years ago, one of the former Editors of this journal launched "a call to action"(E. F. Taylor, Am. J. Phys. 71, 423-425 (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 the 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.
"a call to action": Schrödinger's representation of quantum mechanics via Hamilton's principle
Marrocco M.
2023-01-01
Abstract
A few years ago, one of the former Editors of this journal launched "a call to action"(E. F. Taylor, Am. J. Phys. 71, 423-425 (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 the 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
