ABSTRACT
The Hamilton-Jacobi (HJ) equation for a one-dimensional system is obtained by considering the canonical transformation (q,p) → (Q,P ) so that the old Hamiltonian H maps to a trivialized one, that is H˜ = 0. The old and new momenta are expressed in terms of the generating function of such a transformation, the Hamilton’s principal function p = ∂Scl
∂q , P = cnst = − ∂Scl
∂Q |Q=cnst that satisfies the classical HJ equation
H
( q,p = ∂S
∂q , t
) + ∂S
∂t = 0.
