Ambiguities on the Hamiltonian formulation of the free falling particle with quadratic dissipation

Details Ambiguities on the Hamiltonian formulation of the free falling particle with quadratic dissipation Ambiguities on the Hamiltonian formulation of the free falling particle with quadratic dissipation

2007-10-16

arxiv.org/abs/0710.3123v1

Physics

Quantum Physics

12 pages, 1 figure (ps)

Scientific paper

For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe the dynamics of the same classical system. However, their quantization and the associated statistical mechanics (for an ensemble of particles) describe two completely different quantum and statistical systems. This is shown at first order in the dissipative parameter.

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