Solution of the Hamilton – Jacobi Equation in a Central Potential Using the Separation of Variables Method with Staeckel Boundary Conditions

Abstract

This manuscript aims at solving Hamilton-Jacobi equation in a central potential using the separation of variables technique with Staeckel boundary conditions. Our results show that the Hamilton – Jacobi variables can be completely separated, which agrees with
other results employing different methods.

Keywords: Lagrangian mechanics, Hamilton-Jacobi, Staeckel boundary conditions, Staeckel matrix, Staeckel vector, Hamilton's characteristic function, Hamilton's principal function.