Canonical transformation harmonic oscillator

1. What is canonical transformation explain?
2. How do you calculate canonical transformation?
3. What is the point of canonical transformations?

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.

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.

What is the point of canonical transformations?

Canonical transformations allow us to change the phase-space coordinate system that we use to express a problem, preserving the form of Hamilton's equations. If we solve Hamilton's equations in one phase-space coordinate system we can use the transformation to carry the solution to the other coordinate system.