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  2. Hamiltonian (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_(quantum...

    The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...

  3. Hamiltonian mechanics - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_mechanics

    The transformed Hamiltonian depends only on the G i, and hence the equations of motion have the simple form ˙ =, ˙ = for some function F. [9] There is an entire field focusing on small deviations from integrable systems governed by the KAM theorem .

  4. Equipartition theorem - Wikipedia

    en.wikipedia.org/wiki/Equipartition_theorem

    The (Newtonian) kinetic energy of a particle of mass m, velocity v is given by = | | = (+ +), where v x, v y and v z are the Cartesian components of the velocity v.Here, H is short for Hamiltonian, and used henceforth as a symbol for energy because the Hamiltonian formalism plays a central role in the most general form of the equipartition theorem.

  5. Molecular Hamiltonian - Wikipedia

    en.wikipedia.org/wiki/Molecular_Hamiltonian

    By quantizing the classical energy in Hamilton form one obtains the a molecular Hamilton operator that is often referred to as the Coulomb Hamiltonian. This Hamiltonian is a sum of five terms. This Hamiltonian is a sum of five terms.

  6. Hamiltonian system - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_system

    and thus the Hamiltonian is a constant of motion, whose constant equals the total energy of the system: =. Examples of such systems are the undamped pendulum , the harmonic oscillator , and dynamical billiards .

  7. Hamiltonian field theory - Wikipedia

    en.wikipedia.org/wiki/Hamiltonian_field_theory

    The Hamiltonian for a system of discrete particles is a function of their generalized coordinates and conjugate momenta, and possibly, time. For continua and fields, Hamiltonian mechanics is unsuitable but can be extended by considering a large number of point masses, and taking the continuous limit, that is, infinitely many particles forming a continuum or field.

  8. Action (physics) - Wikipedia

    en.wikipedia.org/wiki/Action_(physics)

    In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1]

  9. Hamilton's principle - Wikipedia

    en.wikipedia.org/wiki/Hamilton's_principle

    Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.