- #61
Dickfore
- 2,987
- 5
yes. the minus sign is redundant.
Landau Quantization: Classical Particle Motion in a Uniform Magnetic Field
- Thread starter Sonny Liston
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- Landau Quantization
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Homework Help Overview
The problem involves a classical particle with charge q and mass m moving in a uniform magnetic field in two dimensions. The discussion focuses on understanding the trajectory of the particle, evaluating the classical action along that trajectory, and determining the magnetic flux as a function of energy.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- Participants discuss the Lorentz force law and its implications for the particle's trajectory, questioning how energy affects the trajectory. There are attempts to derive the equations of motion using Hamiltonian dynamics and to express the Lagrangian for the system. Some participants express confusion regarding the vector potential and its relation to the magnetic field.
Discussion Status
The discussion is ongoing, with participants exploring different interpretations of the vector potential and its implications for the magnetic field. Some guidance has been provided regarding the use of the Landau gauge and the formulation of the Lagrangian, but there is no explicit consensus on the trajectory or the evaluation of the classical action.
Contextual Notes
Participants are grappling with the implications of energy on the trajectory and the correct formulation of the vector potential. There are references to class notes and textbooks, indicating reliance on external sources for clarification. The discussion also highlights the concept of gauge invariance in the context of vector potentials.
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