The Hamiltonian operator (Ĥ) in quantum mechanics represents the total energy of a system. It includes both kinetic and potential energy. When the Hamiltonian acts on a wave function ψ, it gives the system’s total energy as an eigenvalue:

Ĥψ = Eψ

The Hamiltonian is central to the Schrödinger equation and determines how a quantum system evolves.

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