In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases. It is usually denoted by H, also Ȟ or Ĥ. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
The Hamiltonian is named after William Rowan Hamilton, who also created a revolutionary reformation of Newtonian mechanics, now called Hamiltonian mechanics, that is important in quantum physics.

https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)