An effective force between two nucleons used to analyze scattering data can be derived from a non-relativistic Hamiltonian that depends only on the relative coordinate r = |r₁ − r₂| between the nucleons and the corresponding radial momentum p:

(a) Treat r and p as canonically conjugate and derive the corresponding Lagrangian L = L(r, ṙ).
(b) Show that the effective Newton’s law force between the nucleons depends on and ṙ as well as ƒ(r) and g(r).

H (r, p) = p 2m +g(r)+pf (r).