Canonical transformation solved examples

1. How do you calculate canonical transformation?
2. How to find a generating function for a canonical transformation?
3. What is canonical transformation explain?
4. What is canonical transformation in classical mechanics?

How do you calculate canonical transformation?

If λ = 1 then the transformation is canonical, which is what we will study. If λ = 1 then the transformation is extended canonical, and the results from λ = 1 can be recovered by rescaling q and p appropriately.

How to find a generating function for a canonical transformation?

First of all pick a type of generating function. Say F1(q,Q) then the corresponding relations are ∂F1∂q=p. and ∂F1∂Q=−P The general method is to write p and P in terms of the variables of your function which in this case are q and Q. Then you use the relations and integrate to find the generating function.

What is canonical transformation explain?

Example. A canonical transformation is often defined by saying that it must transform any Hamiltonian flow into another one, and this seems to be exactly the definition of a certain normalizer.

What is canonical transformation in classical mechanics?

A canonical transformation is a phase-space coordinate transformation and an associated transformation of the Hamiltonian such that the dynamics given by Hamilton's equations in the two representations describe the same evolution of the system.