Definition for "Hamiltonian" in the Quantum Dictionary

- Modern Physics -

Quantum Mechanics Dictionary

A dynamical concept defining how quantum states or operators change with time under a specified Hamiltonian. It governs time propagation, phase accumulation, and the effect of driving or slowly varying parameters when present. It does not ensure accurate prediction without correct initial conditions, boundary conditions, and validated model assumptions.

Natural & Formal Sciences Dictionary

A scalar function or linear operator that generates deterministic time evolution of a physical system by pairing canonical coordinates with their conjugate momenta (classical) or by acting as the energy operator in unitary quantum dynamics.