Hamiltonian: meaning, definitions and examples

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Hamiltonian

 

[ ˌhæmɪlˈtoʊniən ]

Noun
Context #1 | Noun

physics

A Hamiltonian is a mathematical operator corresponding to the total energy of a system in quantum mechanics. It is used to describe the dynamics of the system and is an essential concept in theoretical physics.

Synonyms

energy operator, total energy operator

Examples of usage

  • The Hamiltonian operator plays a crucial role in determining the behavior of quantum systems.
  • In quantum mechanics, the time evolution of a system is governed by the Hamiltonian.
Context #2 | Noun

mathematics

In mathematics, a Hamiltonian is a function used to describe the state of a dynamic system in terms of position and momentum variables. It is often used in classical mechanics and differential equations.

Synonyms

Hamilton function, Hamiltonian function

Examples of usage

  • The Hamiltonian function can be used to derive the equations of motion for a physical system.
  • Hamiltonian mechanics provides a powerful framework for understanding the behavior of dynamical systems.

Translations

Translations of the word "Hamiltonian" in other languages:

🇵🇹 Hamiltoniano

🇮🇳 हैमिल्टोनियन

🇩🇪 Hamiltonian

🇮🇩 Hamiltonian

🇺🇦 Гамільтоніан

🇵🇱 Hamiltonian

🇯🇵 ハミルトニアン

🇫🇷 Hamiltonien

🇪🇸 Hamiltoniano

🇹🇷 Hamiltonyen

🇰🇷 해밀토니안

🇸🇦 هاميلتوني

🇨🇿 Hamiltonián

🇸🇰 Hamiltonián

🇨🇳 哈密顿量

🇸🇮 Hamiltonian

🇮🇸 Hamiltonian

🇰🇿 Гамильтониан

🇬🇪 ჰამილტონიანი

🇦🇿 Hamiltonian

🇲🇽 Hamiltoniano

Word origin

The term 'Hamiltonian' is named after Sir William Rowan Hamilton, an Irish mathematician, and physicist who introduced the concept in the 19th century. Hamilton's work on mechanics and optics laid the foundation for the development of the Hamiltonian formalism in physics and mathematics.