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Determination of Lagrangians from Equations of Motion and Commutator Brackets (1999)

Bracken, Paul

Springer

Acta applicandae mathematicae 57 (1999), S. 83-103

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ISSN: 1572-9036

Keywords: Lagrangian ; Hamiltons principle ; commutator brackets

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The question as to whether a given set of equations, which govern the dynamical evolution of a system, determine a Lagrangian is considered. This problem, which has come to be known as the inverse problem of the calculus of variations, is reviewed and theorems which contain systems of partial differential equations which determine a type of self-adjointness are developed. It is shown that, given a reasonable form for the classical correspondence, the usual quantum commutator brackets can be expressed in terms of classical quantities which satisfy a particular form of these equations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1006271332516

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