Hamiltonian operator

The Hamiltonian operator is a fundamental concept in physics that describes the total energy of a system, including both kinetic (motion) and potential (position-based) energies. In quantum mechanics, it mathematically represents how a system evolves over time, acting on the wave function to determine the system's possible energy levels. Think of it as a mathematical tool that encapsulates all the energy information of a system, guiding predictions about its behavior. Essentially, the Hamiltonian is central to understanding and calculating the dynamics and properties of physical systems at the quantum level.