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## Homework Statement

How do I go about finding the most general form of the canonical transformation of the form

Q = f(q) + g(p)

P = c[f(q) + h(p)]

where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in the new and old system

## Homework Equations

{Q,Q}={P,P}=0 {Q,P}=1

## The Attempt at a Solution

I arrived at a function

c.f'(q)[h'(p)-g'(p)]=1

I don't know how to get further to prove canonicity