The Liouville theorem as a problem of common eigenfunctions
Abstract
It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of the Hamilton--Jacobi equation can be formulated as the problem of finding common eigenfunctions of $n$ constants of motion in involution, where $n$ is the number of degrees of freedom of the system.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2015
- DOI:
- 10.48550/arXiv.1503.06789
- arXiv:
- arXiv:1503.06789
- Bibcode:
- 2015arXiv150306789T
- Keywords:
-
- Physics - Classical Physics