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  2. Ground state - Wikipedia

    en.wikipedia.org/wiki/Ground_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. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum.

  3. Variational method (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Variational_method...

    In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals. [1] The basis for this method is the variational principle. [2] [3]

  4. Zero-point energy - Wikipedia

    en.wikipedia.org/wiki/Zero-point_energy

    In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state ...

  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. Stationary state - Wikipedia

    en.wikipedia.org/wiki/Stationary_state

    For example, according to simple (nonrelativistic) quantum mechanics, the hydrogen atom has many stationary states: 1s, 2s, 2p, and so on, are all stationary states. But in reality, only the ground state 1s is truly "stationary": An electron in a higher energy level will spontaneously emit one or more photons to decay into the ground state. [3]

  7. Degenerate energy levels - Wikipedia

    en.wikipedia.org/wiki/Degenerate_energy_levels

    In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system.Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement.

  8. Variational quantum eigensolver - Wikipedia

    en.wikipedia.org/wiki/Variational_quantum_eigen...

    In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems.It is a hybrid algorithm that uses both classical computers and quantum computers to find the ground state of a given physical system.

  9. Quantum harmonic oscillator - Wikipedia

    en.wikipedia.org/wiki/Quantum_harmonic_oscillator

    The ground state energy is N times the one-dimensional ground energy, as we would expect using the analogy to N independent one-dimensional oscillators. There is one further difference: in the one-dimensional case, each energy level corresponds to a unique quantum state.