Can I substitute the new coordinates in the old hamiltonian?

1. Mar 27, 2015

Coffee_

We went over this concept quite fast in class and there is one thing that confused me:

When transforming from a set of $q_i$ and $p_i$to $Q_i$ and $P_i$, if one checks that the transormations are canonical the new Hamiltonian $K(Q_i, P_i)$ obeys exactly the same equations.This has been proven.

Question: How does one in general find this new Hamiltonian $K(Q_i, P_i)$? I have gotten the impression that it's not as easy as just substituting the transformations into the old coordinates, or is it?

2. Mar 28, 2015

Orodruin

Staff Emeritus
The Hamiltonian is a function on phase space. It does not matter what coordinates you use to express it.

3. Mar 28, 2015

Coffee_

This means that I can just substitute my old coordinates in function of the new coordinates into my old hamiltonian to get the new hamiltonian?