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Quantum mechanics From Wikipedia, the free encyclopedia You have new messages (last change). Jump to: navigation, search Quantum mechanics go j5 Uncertainty principle Introduction · Mathematical formulation [show]Background Classical mechanics Old quantum theory Interference · Bra-ket notation Hamiltonian [show]Fundamental concepts Quantum state · Wave function Superposition · Entanglement

Measurement · Uncertainty Exclusion · Duality Decoherence · Ehrenfest theorem · Tunneling [show]Experiments Double-slit experiment Davisson–Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Elitzur-Vaidman bomb-tester Quantum eraser [show]Formulations Schrödinger picture Heisenberg picture Interaction picture Matrix mechanics Sum over histories [show]Equations Schrödinger equation Pauli equation Klein–Gordon equation Dirac equation Bohr Theory and Balmer-Rydberg Equation [show]Interpretations Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional [show]Advanced topics Quantum information science scattering theory Quantum field theory [show]Scientists Planck · Einstein · Bohr · Sommerfeld · Bose · Kramers · Heisenberg· Born · Jordan · Pauli · Dirac · de Broglie ·Schrödinger · von Neumann · Wigner · Feynman · Candlin · Bohm · Everett · Bell · Wien This box: view • talk • edit Fig. 1: Probability densities corresponding to the wavefunctions of an electron in a hydrogen atom possessing definite energy levels (increasing from the top of the image to the bottom: n = 1, 2, 3, ...) and angular momentum (increasing across from left to right: s, p, d,...). Brighter areas correspond to higher probability density in a position measurement. Wavefunctions like these are directly comparable to Chladni's figures of acoustic modes of vibration classical physics and are indeed modes of oscillation as well: they possess a sharp energy and thus a keen frequency. The angular momentum and energy are quantized, and only take on discrete values like those shown (as is the case for resonant frequencies in acoustics).Quantum mechanics (QM) is a set of principles describing physical reality at the atomic level of matter (molecules and atoms) and the subatomic (electrons, protons, and even smaller particles). These descriptions include the simultaneous wave-like and particle-like behavior of both matter[1] and radiation[2] ("wave–particle duality"). In the quantum mechanics of a subatomic particle, one can never specify its state, such as its simultaneous location and velocity, with complete certainty (this is called the Heisenberg uncertainty principle — see its formula in the box to the right).

Certain systems, however, do exhibit quantum mechanical effects on a larger scale; superfluidity (the frictionless flow of a liquid at temperatures near absolute zero) is one well-known example. Quantum theory also provides accurate descriptions for many previously unexplained phenomena such as black body radiation and the stability of electron orbits. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures.[3]

Even so, classical physics often can be a good approximation to results otherwise obtained by quantum physics, typically in circumstances with large numbers of particles or large quantum numbers. (However, some open questions remain in the field of quantum chaos.)

Contents [hide] 1 Overview 2 History 3 Quantum mechanics and classical physics 4 Theory 4.1 Mathematical formulation 4.2 Interactions with other scientific theories 5 Example 6 Attempts at a unified field theory 7 Relativity and quantum mechanics 8 Applications 9 Philosophical consequences 10 See also 11 Notes 12 References 13 Further reading 14 External links

[edit] Overview Main article: Introduction to quantum mechanics The word quantum is Latin for "how great" or "how much."[4] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). The discovery that waves have discrete energy packets (called quanta) that behave in a manner similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call quantum mechanics. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Albert Einstein, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli, David Hilbert, and others.[5] Some fundamental aspects of the theory are still actively studied.[6]

Quantum mechanics is essential to understand the behavior of systems at atomic length scales and smaller. For example, if classical mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an uncertain, non-deterministic "smeared" (wave-particle wave function) orbital path around or "through" the nucleus, defying classical electromagnetism.[7]

Quantum mechanics was initially developed to provide a better explanation of the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom was developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by Maxwell's laws of classical electromagnetism.[8]

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space.[9] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds,” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate.[10]

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave–particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain “macroscopic quantum systems” such as superconductors and superfluids.[11]

Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (I) the quantization (discretization) of certain physical quantities, (II) wave-particle duality, (III) the uncertainty principle, and (IV) quantum entanglement. Each of these phenomena is described in detail in subsequent sections.[11]