Question

What is conjugate of momentum and position in in hamiltonian?

Answer 1

Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals,[1][2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle—between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty relation corresponds to the symplectic form.