Quantum gravity (QG) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics (describing three of the four known fundamental interactions) with general relativity (describing the fourth, gravity). It is hoped that development of such a theory would unify into a single mathematical framework all fundamental interactions and to describe all known observable interactions in the universe, at both subatomic and cosmological scales.

Such a theory of quantum gravity would yield the same experimental results as ordinary quantum mechanics in conditions of weak gravity (gravitational potentials much less than c2) and the same results as Einsteinian general relativity in phenomena at scales much larger than individual molecules (action much larger than reduced Planck's constant), but moreover be able to predict the outcome of situations where both quantum effects and strong-field gravity are important (at the Planck scale, unless large extra dimension conjectures are correct).

If the theory of quantum gravity also achieves a grand unification of the other known interactions, it is referred to as a theory of everything (TOE).

Motivation for quantizing gravity comes from the remarkable success of the quantum theories of the other three fundamental interactions, and from experimental evidence suggesting that gravity can be made to show quantum effects. Although some quantum gravity theories such as string theory and other unified field theories (or 'theories of everything') attempt to unify gravity with the other fundamental forces, others such as loop quantum gravity make no such attempt; they simply quantize the gravitational field while keeping it separate from the other forces.

Observed physical phenomena can be described well by quantum mechanics or general relativity, without needing both. This can be thought of as due to an extreme separation of mass scales at which they are important. Quantum effects are usually important only for the "very small", that is, for objects no larger than typical molecules. General relativistic effects, on the other hand, show up mainly for the "very large" bodies such as collapsed stars. (Planets' gravitational fields, as of 2011, are well-described by linearized gravity except for Mercury's perihelion precession; so strong-field effects—any effects of gravity beyond lowest nonvanishing order in φ/c2—have not been observed even in the gravitational fields of planets and main sequence stars). There is a lack of experimental evidence relating to quantum gravity, and classical physics adequately describes the observed effects of gravity over a range of 50 orders of magnitude of mass, i.e., for masses of objects from about 10⁻²³ to 10³⁰ kg.

The Quantum Harmonic Oscillator (QHD) is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.

See also:
https://en.wikipedia.org/wiki/Quantum_gravity
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

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