**Quantum mechanics** (QM – also known as **quantum physics**, or **quantum theory**) is a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant. Quantum mechanics departs from classical mechanics primarily at the *quantum realm* of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual *particle-like* and *wave-like* behavior and interactions of energy and matter.

In advanced topics of quantum mechanics, some of these behaviors are macroscopic and only emerge at extreme (i.e., very low or very high) energies or temperatures. The name *quantum mechanics* derives from the observation that some physical quantities can change only in *discrete* amounts (Latin *quanta*), and not in a continuous (*cf.* analog) way. For example, the angular momentum of an electron bound to an atom or molecule is quantized. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects.

The mathematical formulations of quantum mechanics are abstract. A mathematical function called the wavefunction provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator, and the mathematics is akin to that describing acoustic resonance. Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics—for instance, the ground state in a quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, as opposed to a more "traditional" system that is thought of as simply being at rest, with zero kinetic energy. Instead of a traditional static, unchanging zero state, quantum mechanics allows for far more dynamic, chaotic possibilities, according to John Wheeler.

The earliest versions of quantum mechanics were formulated in the first decade of the 20th century. At around the same time, the atomic theory and the corpuscular theory of light (as updated by Einstein) first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively. Early quantum theory was significantly reformulated in the mid-1920s by Werner Heisenberg, Max Born and Pascual Jordan, who created matrix mechanics; Louis de Broglie and Erwin Schrodinger (Wave Mechanics); and Wolfgang Pauli and Satyendra Nath Bose (statistics of subatomic particles). And the Copenhagen interpretation of Niels Bohr became widely accepted. By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann, with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality, and philosophical speculation about the role of the observer. Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines, such as quantum chemistry, quantum electronics, quantum optics, and quantum information science. Much 19th century physics has been re-evaluated as the "classical limit" of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories.

Read more about Quantum Mechanics: History, Mathematical Formulations, Mathematically Equivalent Formulations of Quantum Mechanics, Interactions With Other Scientific Theories, Philosophical Implications, Applications

### Other articles related to "quantum mechanics, quantum, mechanics":

**Quantum Mechanics**

... involving large mass objects in fairly large regions of spacetime whereas

**quantum mechanics**is generally reserved for scenarios at the atomic scale (small spacetime regions) ... general relativity predicts a smooth, flowing surface, while

**quantum mechanics**predicts a random, warped surface, neither of which are anywhere near compatible ... length, with extremely small variances, which completely ignores the

**quantum**mechanical predictions of Planck-scale length dimensional warping ...

... A versatile theoretical physicist, Bethe also made important contributions to

**quantum**electrodynamics, nuclear physics, solid-state physics and astrophysics ... David Bohm (agnostic) - American-born British

**quantum**physicist who contributed to theoretical physics, philosophy of mind, neuropsychology ... to understanding atomic structure and

**quantum mechanics**, for which he received the Nobel Prize in Physics in 1922 ...

... After publishing a popular textbook on

**Quantum Mechanics**which adhered entirely to the Copenhagen orthodoxy, Bohm was persuaded by Einstein to take a critical look ... The result was 'A Suggested Interpretation of the

**Quantum**Theory in Terms of "Hidden Variables" I and II' ... to this, in the way Brownian motion disturbs Newtonian

**mechanics**) ...

... state itself, or on the subsequent system dynamics." In

**quantum mechanics**, the Leggett–Garg inequality is violated, meaning that the time evolution of a system cannot be understood classically ... Here

**quantum**entanglement plays the central role ... which can not be obtained in the standard Copenhagen Interpretation of

**quantum mechanics**in its various formulations ...

**Quantum Mechanics**- Examples - Harmonic Oscillator

... Main article

**Quantum**harmonic oscillator As in the classical case, the potential for the

**quantum**harmonic oscillator is given by This problem can be solved either by ...

### Famous quotes containing the words mechanics and/or quantum:

“It is only the impossible that is possible for God. He has given over the possible to the *mechanics* of matter and the autonomy of his creatures.”

—Simone Weil (1909–1943)

“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense *quantum* sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”

—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)