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Perturbation theory

Index Perturbation theory

Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. [1]

58 relations: Ab initio quantum chemistry methods, Algebraic equation, Approximation theory, Astrometry, Average, Carl Friedrich Gauss, Celestial mechanics, Cosmological perturbation theory, Coupled cluster, Differential equation, Discovery of Neptune, Dynamic nuclear polarisation, Eigenvalue perturbation, Equation solving, Equations of motion, Eric Vanden-Eijnden, Fermi's golden rule, Feynman diagram, Formal power series, Function (mathematics), General relativity, Ground state, Hamiltonian (quantum mechanics), Harmonic oscillator, Homotopy analysis method, Interaction, Interval finite element, Isaac Newton, Johann Gottfried Galle, Joseph-Louis Lagrange, Kepler's laws of planetary motion, Linear equation, Lyapunov stability, Moon, Newton's law of universal gravitation, Newton's laws of motion, Numerical analysis, Orbit of the Moon, Order of approximation, Oxford University Press, Paul Dirac, Perturbation theory (quantum mechanics), Pierre-Simon Laplace, Proceedings of the Royal Society, Quantum mechanics, Siméon Denis Poisson, Singular perturbation, Solar System, Statistical mechanics, Structural stability, ..., Sun, Thermodynamic free energy, Three-body problem, Trajectory, Two-body problem, Uranus, Urbain Le Verrier, Wave equation. Expand index (8 more) »

Ab initio quantum chemistry methods

Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Approximation theory

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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Astrometry

Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies.

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Average

In colloquial language, an average is a middle or typical number of a list of numbers.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

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Cosmological perturbation theory

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the big bang model.

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Coupled cluster

Coupled cluster (CC) is a numerical technique used for describing many-body systems.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Discovery of Neptune

The planet Neptune was mathematically predicted before it was directly observed.

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Dynamic nuclear polarisation

Dynamic nuclear polarization (DNP) results from transferring spin polarization from electrons to nuclei, thereby aligning the nuclear spins to the extent that electron spins are aligned.

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Eigenvalue perturbation

In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system that is perturbed from one with known eigenvectors and eigenvalues.

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Equation solving

In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.

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Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.

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Eric Vanden-Eijnden

Eric Vanden-Eijnden is a professor of mathematics at the Courant Institute of Mathematical Sciences, New York University.

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Fermi's golden rule

In quantum physics, Fermi's golden rule is a formula that describes the transition rate (probability of transition per unit time) from one energy eigenstate of a quantum system into other energy eigenstates in a continuum, effected by a weak perturbation.

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Feynman diagram

In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles.

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Formal power series

In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Ground state

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

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Hamiltonian (quantum mechanics)

In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.

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Harmonic oscillator

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: where k is a positive constant.

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Homotopy analysis method

The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations.

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Interaction

Interaction is a kind of action that occur as two or more objects have an effect upon one another.

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Interval finite element

In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Johann Gottfried Galle

Johann Gottfried Galle, 1880 Galle's signature Memorial plaque in Wittenberg Johann Gottfried Galle (9 June 1812 – 10 July 1910) was a German astronomer from Radis, Germany, at the Berlin Observatory who, on 23 September 1846, with the assistance of student Heinrich Louis d'Arrest, was the first person to view the planet Neptune and know what he was looking at.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.

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Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

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Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

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Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Orbit of the Moon

The Moon orbits Earth in the prograde direction and completes one revolution relative to the stars in about 27.322 days (a sidereal month) and one revolution relative to the Sun in about 29.530 days (a synodic month).

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Order of approximation

In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Paul Dirac

Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.

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Perturbation theory (quantum mechanics)

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one.

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Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Proceedings of the Royal Society

Proceedings of the Royal Society is the parent title of two scientific journals published by the Royal Society.

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Quantum mechanics

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 scales of energy levels of atoms and subatomic particles.

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Siméon Denis Poisson

Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician, engineer, and physicist, who made several scientific advances.

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Singular perturbation

In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero.

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Solar System

The Solar SystemCapitalization of the name varies.

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Statistical mechanics

Statistical mechanics is one of the pillars of modern physics.

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Structural stability

In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact ''C''1-small perturbations).

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Sun

The Sun is the star at the center of the Solar System.

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Thermodynamic free energy

The thermodynamic free energy is the amount of work that a thermodynamic system can perform.

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Three-body problem

In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics.

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Trajectory

A trajectory or flight path is the path that a massive object in motion follows through space as a function of time.

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Two-body problem

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other.

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Uranus

Uranus is the seventh planet from the Sun.

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Urbain Le Verrier

Urbain Jean Joseph Le Verrier (11 March 1811 – 23 September 1877) was a French mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using only mathematics.

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Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.

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First-order non-singular perturbation theory, Higher order terms, Higher-order terms, Pertubation Theory, Perturbation (mathematics), Perturbation Theory, Perturbation analysis, Perturbation methods, Perturbation series, Perturbation theory (mathematics), Singular perturbation theory, Small perturbations.

References

[1] https://en.wikipedia.org/wiki/Perturbation_theory

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