In classical mechanics, the sum of kinetic and potential energy functions (i.e., the total energy); in quantum mechanics, the corresponding linear Hermitian operator.

a mathematical operator that, when applied to such things as "wave functions," describes the total energy of a physical system

The operator H (consisting of potential and kinetic energy terms) which describes which operations are to be carried out on the wavefunction in the Schrödinger equation H. ("an operator is a symbol that tells you to do something to whatever follows the symbol" McQuarrie, 1983)

Mathematical operator used in the Schroedinger Equation

Matrix of bare nucleus, 0 e- Fock Matrix. Matrix that operates on wavefunction to calculate the energy in Schrödingers equation.

In quantum mechanics, the Hamiltonian H is the observable corresponding to the total energy of the system. As with all observables, the spectrum of the Hamiltonian is the set of possible outcomes when one measures the total energy of a system. Like any other self adjoint operator, the spectrum of the Hamiltonian can be decomposed, via its spectral measures, into pure point, absolutely continuous, and singular parts.

The Hamiltonian of optimal control theory was developed by L. S. Pontryagin as part of his minimum principle. It was inspired by, but is distinct from, the Hamiltonian of classical mechanics.