A quantum route to Hamilton–Jacobi equation: comments and remarks
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
Streszczenie
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.
Autorzy
- 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