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Il Nuovo Cimento B (1971-1996)

, Volume 90, Issue 2, pp 143–160 | Cite as

An attempt to construct quantum mechanics from Newton equations

  • R. Hojman
  • S. Hojman
Article

Summary

We present one scheme for quantizing classical theories starting from their equations of motion. The procedure is such that the well-established quantum-mechanical results for conservative systems are recovered by construction. The method provides a unique way of quantizing classical systems irrespective of the nonexistence (or multiplicity) of Lagrangians for their equations of motion. We exhibit the quantization of the one-dimensional damped harmonic oscillator following this scheme.

Keywords

PACS. 03.65.Ca Formalism PACS. 03.20. Classical mechanics of discrete systems: general mathematical aspects 

Riassunto

Si presenta uno schema per quantizzare teorie classiche partendo dalla loro equazioni di moto. La procedura è tale che i ben definiti risultati quantomeccanici per sistemi conservativi sono reinstaurati per costruzione. Il metodo fornisce un modo unico per quantizzare sistemi classici senza tener conto della non esistenza (o moltiplicità) delle lagrangiane per le loro equazioni di moto. Si mostra la quantizzazione dell’oscillatore armonico unidimensionale smorzato seguendo quasto schema.

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Copyright information

© Società Italiana di Fisica 1985

Authors and Affiliations

  • R. Hojman
    • 1
    • 2
  • S. Hojman
    • 1
  1. 1.Departmento de FisicaUniversidad de Santiago de ChileSantiagoChile
  2. 2.Centro de Fisica El TraucoSantiagoChile

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