Reparametrization-invariant formulation of classical mechanics and the Schrödinger equation

A. Deriglazov, B. F. Rizzuti

Результат исследований: Материалы для журналаСтатья

4 Цитирования (Scopus)

Аннотация

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 H̃ = pt+H, where H is the usual Hamiltonian and pt is the momentum conjugate to the variable t. Due to reparametrization invariance, H̃ vanishes for any solution, and hence the corresponding quantum-mechanical operator has the property Ĥψ= 0, which is the time-dependent Schrödinger equation, ih∂tψ=Ĥψ. We discuss the quantum mechanics of a relativistic particle as an example.

Язык оригиналаАнглийский
Страницы (с-по)882-885
Число страниц4
ЖурналAmerican Journal of Physics
Том79
Номер выпуска8
DOI
СостояниеОпубликовано - 26 июл 2011
Опубликовано для внешнего пользованияДа

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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