Harry Potter and the Methods of Rationality - Scientific facts

xkcd: Quantum Mechanics In quantum mechanics , the Hamiltonian is the operator corresponding to the total energy of the system. 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 the sum of the kinetic energies of all the particles, plus the potential energy of the particles associated with the system. For different situations or number of particles, the Hamiltonian is different since it includes the sum of kinetic energies of the particles, and the potential energy function corresponding to the situation. Hamiltonian (quantum mechanics) - Wikipedia, the free encyclopedia  HPMOR - Chapter 2

In quantum physics , unitarity is a restriction on the allowed evolution of quantum systems that ensures the sum of probabilities of all possible outcomes of any event is always 1. More precisely, the operator which describes the progress of a physical system in time must be a unitary operator . When the Hamiltonian is time-independent the unitary operator is . Unitarity (physics) - Wikipedia, the free encyclopedia  Chapter 2