Hamiltonian

A Hamiltonian is a mathematical tool used in physics to describe the total energy of a system, including both its kinetic (motion) and potential (position-related) energies. It helps scientists understand how systems evolve over time, such as particles in a gas or planets orbiting a star. Think of it as an energy blueprint that dictates how a system changes, enabling predictions about future states. In essence, the Hamiltonian provides a comprehensive snapshot of a system's energetic makeup, serving as a foundation for analyzing and solving complex physical problems.