A quantum route to Hamilton–Jacobi equation: comments and remarks

Volume 110 / 2016

José F. Cariñena, Eduardo Martínez, Giuseppe Marmo, Xavier Gràcia, C. Muñoz-Lecanda Banach Center Publications 110 (2016), 41-56 MSC: 35F21, 35Q40, 81Q05. DOI: 10.4064/bc110-0-3

Abstract

We consider the short-wave limit of evolutionary wave equations to derive the Hamilton–Jacobi equation. In particular we consider how to get wave mechanics from the abstract picture on Hilbert spaces. This ‘realisation’ contains an additional ingredient which resembles the classical configuration space. We comment on the fact that Hamilton–Jacobi theory only considers one of the two equations obtained in the appropriate limit. We also comment on the fact that the superposition rule for the linear equation is no longer available for the approximate equation.

Authors

  • José F. CariñenaDepartamento de Física Teórica and IUMA
    Facultad de Ciencias
    Universidad de Zaragoza
    50009 Zaragoza, Spain
    e-mail
  • Eduardo MartínezDepartamento de Matemática Aplicada and IUMA
    Facultad de Ciencias
    Universidad de Zaragoza
    50009 Zaragoza, Spain
    e-mail
  • Giuseppe MarmoDipartimento di Fisica
    Universitá Federico II di Napoli
    and
    INFN, Sezione di Napoli
    Complesso Univ. di Monte Sant’Angelo
    Via Cintia
    80126 Napoli, Italy
    e-mail
  • Xavier GràciaDepartamento de Matemáticas
    Edificio C-3, Campus Norte UPC
    C/Jordi Girona 1
    E-08034 Barcelona, Spain
    e-mail
  • C. Muñoz-LecandaDepartamento de Matemáticas
    Edificio C-3, Campus Norte UPC
    C/Jordi Girona 1
    E-08034 Barcelona, Spain
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image