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  2. Zero-point energy - Wikipedia

    en.wikipedia.org/wiki/Zero-point_energy

    Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. [1] Therefore, even at absolute zero, atoms and molecules retain some vibrational motion.

  3. Vienna Ab initio Simulation Package - Wikipedia

    en.wikipedia.org/wiki/Vienna_Ab_initio...

    The Vienna Ab initio Simulation Package, better known as VASP, is a package written primarily in Fortran for performing ab initio quantum mechanical calculations using either Vanderbilt pseudopotentials, or the projector augmented wave method, and a plane wave basis set. [2]

  4. Ground state - Wikipedia

    en.wikipedia.org/wiki/Ground_state

    Energy levels for an electron in an atom: ground state and excited states. After absorbing energy, an electron may jump from the ground state to a higher-energy excited state. The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system.

  5. Quantum vacuum state - Wikipedia

    en.wikipedia.org/wiki/Quantum_vacuum_state

    The video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversion.. If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement ...

  6. AP World History: Modern - Wikipedia

    en.wikipedia.org/wiki/AP_World_History:_Modern

    AP World History: Modern was designed to help students develop a greater understanding of the evolution of global processes and contacts as well as interactions between different human societies. The course advances understanding through a combination of selective factual knowledge and appropriate analytical skills.

  7. Quantum fluctuation - Wikipedia

    en.wikipedia.org/wiki/Quantum_fluctuation

    3D visualization of quantum fluctuations of the quantum chromodynamics (QCD) vacuum [1]. In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, [2] as prescribed by Werner Heisenberg's uncertainty principle.

  8. Degenerate energy levels - Wikipedia

    en.wikipedia.org/wiki/Degenerate_energy_levels

    The measurable values of the energy of a quantum system are given by the eigenvalues of the Hamiltonian operator, while its eigenstates give the possible energy states of the system. A value of energy is said to be degenerate if there exist at least two linearly independent energy states associated with it.

  9. Fine structure - Wikipedia

    en.wikipedia.org/wiki/Fine_structure

    The fine structure energy corrections can be obtained by using perturbation theory.To perform this calculation one must add three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.