# Quantum mechanics

**quantum physicsquantum mechanicalquantum theoryquantumquantum-mechanicalquantum physicistquantum effectsquantum mechanicquantum phenomenaquantum hypothesis**

Quantum mechanics, (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest – including atomic and subatomic – scales.wikipedia

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### Quantum field theory

**quantum field theoriesquantum fieldquantum theory**

Quantum mechanics, (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest – including atomic and subatomic – scales.

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics (but notably not general relativity's description of gravity) and is used to construct physical models of subatomic particles (in particle physics) and quasiparticles (in condensed matter physics).

### History of quantum mechanics

**History of quantum physicsQuantum Hypothesisquantum mechanics**

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.

The history of quantum mechanics is a fundamental part of the history of modern physics.

### Albert Einstein

**EinsteinEinsteinianA. Einstein**

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. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

### Quantization (physics)

**quantizationquantizedquantize**

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are 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 measured (the uncertainty principle).

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.

### Max Planck

**PlanckMax Karl Ernst Ludwig PlanckPlanck, M.**

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. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Max Karl Ernst Ludwig Planck, ForMemRS (23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.

### Old quantum theory

**quantum theoryBohr–Sommerfeld quantizationBohr-Sommerfeld quantization**

Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others.

The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics.

### Werner Heisenberg

**HeisenbergW. HeisenbergHeisenberg, Werner**

Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics.

### Wave function

**wavefunctionwave functionsnormalized**

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.

A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.

### Max Born

**BornBorn, M.Born M**

Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Max Born ( 11 December 1882 – 5 January 1970) was a German-Jewish physicist and mathematician who was instrumental in the development of quantum mechanics.

### Mathematical formulation of quantum mechanics

**quantum mechanicspostulates of quantum mechanicspostulate of quantum mechanics**

The modern theory is formulated in various specially developed mathematical formalisms.

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics.

### Probability amplitude

**probability densityBorn probabilitytransition amplitude**

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.

In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems.

### Momentum

**conservation of momentumlinear momentummomenta**

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are 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 measured (the uncertainty principle).

Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

### Classical physics

**classicalclassical theoryclassically**

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are 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 measured (the uncertainty principle). Classical physics, the description of physics existing before the formulation of the theory of relativity and of quantum mechanics, describes nature at ordinary (macroscopic) scale.

Most usually classical physics refers to pre-1900 physics, while modern physics refers to post-1900 physics which incorporates elements of quantum mechanics and relativity.

### Angular momentum

**conservation of angular momentumangular momentamomentum**

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are 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 measured (the uncertainty principle).

In quantum mechanics, angular momentum (like other quantities) is expressed as an operator, and its one-dimensional projections have quantized eigenvalues.

### Arnold Sommerfeld

**SommerfeldArnold Johannes Wilhelm SommerfeldA. Sommerfeld**

In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept also introduced by Arnold Sommerfeld. The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Arnold Johannes Wilhelm Sommerfeld, (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics.

### Physics

**physicistphysicalphysicists**

Quantum mechanics, (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest – including atomic and subatomic – scales.

The laws comprising classical physics remain very widely used for objects on everyday scales travelling at non-relativistic speeds, since they provide a very close approximation in such situations, and theories such as quantum mechanics and the theory of relativity simplify to their classical equivalents at such scales.

### Paul Dirac

**DiracPaul Adrien Maurice DiracP. A. M. Dirac**

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics.

### Maxwell's equations

**Maxwell equationsMaxwell equationMaxwell’s equations**

Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations.

Versions of Maxwell's equations based on the electric and magnetic potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.

### Planck's law

**Planck's law of black body radiationPlanck's law of black-body radiationblack-body radiation**

Later, Planck corrected this model using Boltzmann's statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics.

This discovery was a pioneering insight of modern physics and is of fundamental importance to quantum theory.

### John von Neumann

**von NeumannJ. von NeumannNeumann, John von**

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.

### Photon

**photonslight quantaincident photon**

Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle, or quanta (later called the photon), with a discrete quantum of energy that was dependent on its frequency.

Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles.

### Wave

**travelling wavewavestraveling wave**

Some, like the probability waves of quantum mechanics, may be completely static.

### Enrico Fermi

**FermiE. FermiFermi, Enrico**

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and.

He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.

### Matter

**corporealsubstancematerial**

Around 1900–1910, the atomic theory but not the corpuscular theory of light first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively.

However this is only somewhat correct, because subatomic particles and their properties are governed by their quantum nature, which means they do not act as everyday objects appear to act – they can act like waves as well as particles and they do not have well-defined sizes or positions.

### Wolfgang Pauli

**Pauli Wolfgang Pauli’sPauli, Wolfgang**

Wolfgang Ernst Pauli (25 April 1900 – 15 December 1958) was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics.