Constrained Dynamics on an Ellipse
Akshay Chaturvedi, Pichai Ramadevi
TL;DR
This paper reviews Dirac's method for constrained classical particles, then extends it to particles on an ellipse, identifying Dirac brackets and quantum operators for the system.
Contribution
It introduces a novel extension of Dirac's method from circular to elliptical constraints, deriving the corresponding brackets and quantum operators.
Findings
Derived Dirac brackets for an elliptical constraint
Quantized the elliptical constrained system
Extended classical methods to more complex geometries
Abstract
We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly, we identify the corresponding Dirac brackets and determine the quantum operators associated with the fundamental dynamical variables.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Quantum Mechanics and Non-Hermitian Physics · Nonlinear Waves and Solitons