# Quantum mechanics

Wavefunctions of the electron in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations.[1] The brighter areas represent a higher probability of finding the electron.

Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.[2]

Classical physics (the physics existing before quantum mechanics) is a set of fundamental theories which describes nature at ordinary (macroscopic) scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.[3] Quantum mechanics differs from classical physics in that: energy, momentum and other quantities of a system may be restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be known (uncertainty principle).[note 1]

Quantum mechanics gradually arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.

Important applications of quantum theory[5] include quantum chemistry, superconducting magnets, light-emitting diodes, and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA.[6]

1. ^ Born, M. (1926). "Zur Quantenmechanik der Stoßvorgänge". Zeitschrift für Physik. 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. Retrieved 16 December 2008.
2. ^ Feynman, Richard; Leighton, Robert; Sands, Matthew (1964). The Feynman Lectures on Physics, Vol. 3. California Institute of Technology. p. 1.1. ISBN 0201500647.
3. ^ Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics. 82 (9): 896–905. Bibcode:2014AmJPh..82..896J. doi:10.1119/1.4878358.
4. ^ Section 3.2 of Ballentine, Leslie E. (1970), "The Statistical Interpretation of Quantum Mechanics", Reviews of Modern Physics, 42 (4): 358–381, Bibcode:1970RvMP...42..358B, doi:10.1103/RevModPhys.42.358. This fact is experimentally well-known for example in quantum optics (see e.g. chap. 2 and Fig. 2.1 Leonhardt, Ulf (1997), Measuring the Quantum State of Light, Cambridge: Cambridge University Press, ISBN 0 521 49730 2
5. ^ Matson, John. "What Is Quantum Mechanics Good for?". Scientific American. Retrieved 18 May 2016.
6. ^ The Nobel laureates Watson and Crick cited Pauling, Linus (1939). The Nature of the Chemical Bond and the Structure of Molecules and Crystals. Cornell University Press. for chemical bond lengths, angles, and orientations.

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).