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# 6: Charged Particle in Magnetic Field


• 6.1: Charged Particle in a Magnetic Field
Classically, the force on a charged particle in electric and magnetic fields is given by the Lorentz force law and is quite different from the conservative forces from potentials that we have dealt with so far, and the recipe for going from classical to quantum mechanics—replacing momenta with the appropriate derivative operators—has to be carried out with more care. We begin by demonstrating how the Lorentz force law arises classically in the Lagrangian and Hamiltonian formulations.

Thumbnail: Trajectory of a particle with a positive or negative charge q under the influence of a magnetic field B, which is directed perpendicularly out of the screen. (CC SA-BY 3.0; Jaro.p).

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