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Laughlin wavefunction, the Glossary

In condensed matter physics, the Laughlin wavefunction is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas placed in a uniform background magnetic field in the presence of a uniform jellium background when the filling factor of the lowest Landau level is \nu.^[1]

24 relations: Angular momentum, Angular momentum operator, Ansatz, Bessel function, Condensed matter physics, Confluent hypergeometric function, Coulomb's law, Cyclotron resonance, Elementary charge, Expected value, Fermion, Fractional quantum Hall effect, Gaussian units, Ground state, Gyroradius, Jellium, Landau levels, Magnetic field, Nobel Prize in Physics, Planck constant, Quantum Hall effect, Quasiparticle, Robert B. Laughlin, Two-dimensional electron gas.
Hall effect
Quantum phases

Angular momentum

Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum.

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Angular momentum operator

In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum.

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Ansatz

In physics and mathematics, an ansatz (meaning: "initial placement of a tool at a work piece", plural ansatzes or, from German, ansätze) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results.

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Bessel function

Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y.

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Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons.

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Confluent hypergeometric function

In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity.

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Coulomb's law

Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest.

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Cyclotron resonance

Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus moving on a circular path. Laughlin wavefunction and Cyclotron resonance are condensed matter physics.

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Elementary charge

The elementary charge, usually denoted by, is a fundamental physical constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1.

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Fermion

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.

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Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h, where e is the electron charge and h is the Planck constant. Laughlin wavefunction and fractional quantum Hall effect are Hall effect and quantum phases.

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Gaussian units

Gaussian units constitute a metric system of physical units.

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Ground state

The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system.

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Gyroradius

The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field.

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Jellium

Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. Laughlin wavefunction and Jellium are condensed matter physics.

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Landau levels

In quantum mechanics, the energies of cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels.

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Magnetic field

A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

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Nobel Prize in Physics

The Nobel Prize in Physics (Nobelpriset i fysik) is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics.

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Planck constant

The Planck constant, or Planck's constant, denoted by is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.

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Quantum Hall effect

The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhibits steps that take on the quantized values where is the Hall voltage, is the channel current, is the elementary charge and is the Planck constant. Laughlin wavefunction and quantum Hall effect are condensed matter physics, Hall effect and quantum phases.

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Quasiparticle

In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Laughlin wavefunction and quasiparticle are condensed matter physics and quantum phases.

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