Postby schmit.paul » Sun Jan 21, 2007 3:04 pm
oh yeah, CPT, I agree that no physics curriculum should *start* with the Lagrangian formalism, but I think as soon as students have gotten to the point where they can solve basic partial differential equations in physics problems (ie, the point in the curriculum where the Schrodinger equation is introduced), the theoretical basis for working with a Hamiltonian should be given, and the classical context is the best way to approach this. At this point the student has probably already done just about everything there is to do in single particle classical mechanics, short of non-inertial reference frames and complex multibody problems, so I make the assumption that the student at this point has a sufficient "intuition" with classical problems to not be confused sufficiently by an introduction to an alternative theoretical framework. Of course, that may not apply to everybody, but I would have liked to have seen it earlier and worked with it more extensively than just a few weeks at the end of a semester. For one, the prof. in my quantum III class had to derive the canonical momentum and the magnetic vector potential term in the Lagrangian in the classical context before he could discuss how to deal with magnetic fields in quantum, and I felt like that that should have been introduced to us the previous semester in our classical class. The sooner the better, within reason, just to get students more comfortable with it as early as possible. It's like learning a new language- the younger people learn it, the easier it is to pick up and use fluently, before we've been too indoctrinated to solve problems a particular way.