Reparametrization-invariant formulation of classical mechanics and the Schrödinger equation

  title={Reparametrization-invariant formulation of classical mechanics and the Schr{\"o}dinger equation},
  author={Alexei A. Deriglazov and Bruno Rizzuti},
  journal={American Journal of Physics},
Any classical-mechanics system can be formulated in reparametrization-invariant form. That is, we use the parametric representation for the trajectories, x=x(τ) and t=t(τ) instead of x=x(t). We discuss the quantization rules in this formulation and show that some of the rules become clearer. In particular, both the temporal and the spatial coordinates are subject to quantization, and the canonical Hamiltonian in the reparametrization-invariant formulation is proportional to H=pt+H, where H is… 

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