There are three easy tests to check if a transformation is canonical. Note that some multiplicative constants might pop up in certain textbooks, depending on the exact definition of canonical …

Dec 24, 2018 · This would be incorrect. So basically, the canonical commutation relations are sort of like conventional commutation relations. You can use non-canonical transformations, and …

Feb 20, 2019 · That is a smaller class of transformations. Secondly, Symmetries are (active) canonical transformations whose generating function commutes with the Hamiltonian (actually …

Jan 14, 2025 · Of course since the coordinate transformation is canonical we find the same equation by using Hamilton's equations with the transformed Hamiltonian \begin {equation} H' …

Oct 14, 2015 · Can all canonical transformations preserving the symplectic form, Eq. (4), be generated by one of the generating functions? tl;dr: If the first cohomology group of the …

I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from $(q, p)$ to $(Q, P)$ is one that if which the original coordinates …

As is well-known, canonical and symplectic transformations are the same. For a proof [at least in the case of restricted transformations, i.e. transformations without explicit time dependence], …

Find generating function $F_1$ for canonical transformation Ask Question Asked 12 years, 8 months ago Modified 5 years ago

Mar 16, 2022 · In Goldstein's Classical Mechanics (3rd edition) section 9.1, we introduce the generating function method of describing a canonical transformation. We then introduce four …

Feb 23, 2019 · I think it would be really strange if point transformations weren't canonical because in almost all Classical Mechanics textbook some like the following is mentioned: [S]ince there …