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  2. Virial theorem - Wikipedia

    en.wikipedia.org/wiki/Virial_theorem

    In statistical mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path) with that of the total potential energy of the system. Mathematically, the theorem states ...

  3. 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 ...

  4. Kinetic energy - Wikipedia

    en.wikipedia.org/wiki/Kinetic_energy

    The kinetic energy is equal to 1/2 the product of the mass and the square of the speed. In formula form: where is the mass and is the speed (magnitude of the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.

  5. Lagrangian mechanics - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_mechanics

    Lagrangian mechanics describes a mechanical system as a pair (M, L) consisting of a configuration space M and a smooth function within that space called a Lagrangian. For many systems, L = T − V, where T and V are the kinetic and potential energy of the system, respectively.

  6. Action principles - Wikipedia

    en.wikipedia.org/wiki/Action_principles

    The energy function in the action principles is not the total energy (conserved in an isolated system), but the Lagrangian, the difference between kinetic and potential energy. The kinetic energy combines the energy of motion for all the objects in the system; the potential energy depends upon the instantaneous position of the objects and ...

  7. Thomas–Fermi model - Wikipedia

    en.wikipedia.org/wiki/Thomas–Fermi_model

    The kinetic energy expression of Thomas–Fermi theory is also used as a component in more sophisticated density approximation to the kinetic energy within modern orbital-free density functional theory. Working independently, Thomas and Fermi used this statistical model in 1927 to approximate the distribution of electrons in an atom.

  8. Maxwell–Boltzmann distribution - Wikipedia

    en.wikipedia.org/wiki/Maxwell–Boltzmann...

    Maxwell–Boltzmann. In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell (ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move ...

  9. Bernoulli's principle - Wikipedia

    en.wikipedia.org/wiki/Bernoulli's_principle

    The energy entering through A 1 is the sum of the kinetic energy entering, the energy entering in the form of potential gravitational energy of the fluid, the fluid thermodynamic internal energy per unit of mass (ε 1) entering, and the energy entering in the form of mechanical p dV work: = (+ + +) where Ψ = gz is a force potential due to the ...

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