Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples

Chung-Ru Lee

Published 2024-06-16Version 1

In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first order evolutionary equations in the phase space coordinates. We state the criterion on the evolution matrix for a Hamiltonian to exist. In addition, the proof is constructive and an explicit Hamiltonian with accompanied symplectic structure can be obtained. As an application, we will study a class of PT-symmetric systems for illustration.