Hamiltonian

Podcast 1 · Introduction

Hamiltonian

A documentary-style narration: origin, meaning, and feel.

Part of speech

noun and adjective

Pronunciation

ham-il-TOH-nee-un  /ˌhæmɪlˈtəʊnɪən/

Definition

As a noun: in physics and mathematics, the function that represents the total energy of a system, used in Hamiltonian mechanics to describe the evolution of a physical system over time. As an adjective: relating to the physicist and mathematician Sir William Rowan Hamilton or to Hamiltonian mechanics.

Plain meaning

In physics, the Hamiltonian is a mathematical function that represents the total energy of a physical system. It is the central object of Hamiltonian mechanics — a reformulation of classical mechanics that has proved essential in quantum physics.

Register

Technical and specialised. Hamiltonian is used in physics, mathematics, and engineering contexts. It is not everyday vocabulary but is widely encountered by anyone studying physics beyond introductory level.