A Lagrangian that yields equations of motion for a damped simple harmonic oscillator is shown not to describe this system, but a completely different physical system. Thus, we have a simple counterexample to the statement: ’’If a Lagrangian gives the correct equations of motion for a given system then the Lagrangian describes the system.’’ We also construct a physical system that the Lagrangian describes and derive some of its properties. The quantum theory based on the above Lagrangian has been used to attempt to discuss the quantum theory of dissipation. This is, however, incorrect since the system the Lagrangian describes has no dissipation.
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© 1979 American Association of Physics Teachers.
1979
American Association of Physics Teachers
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