The Hamiltonian

The 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) energy. It serves as a fundamental equation in classical and quantum mechanics to predict how systems evolve over time. Essentially, it encapsulates everything needed to understand the dynamics of particles, molecules, or fields by providing a comprehensive energy framework. By analyzing the Hamiltonian, scientists can determine how a system will behave, change, or respond under different conditions.