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Trigonometric Rosen–Morse potential, the Glossary

The trigonometric Rosen–Morse potential, named after the physicists Nathan Rosen and Philip M. Morse, is among the exactly solvable quantum mechanical potentials.^[1]

57 relations: Albert Einstein, Angular momentum operator, Boltzmann constant, Cartesian coordinate system, Color confinement, Conformal symmetry, Coupling constant, De Sitter invariant special relativity, Degrees of freedom (mechanics), Dipole, Direct numerical simulation, Direct product, Divergence theorem, Electric dipole moment, Electric potential, Electromagnetism, Electrostatics, Erwin Schrödinger, Euclidean space, Ewald summation, Fluid dynamics, Gauge theory, Gauss's law, Gegenbauer polynomials, Geodesic, Hadron, Hadron spectroscopy, Harmonic function, Hydrogen atom, Hyperboloid, Laplace operator, Laplace–Beltrami operator, Light cone, List of quantum-mechanical potentials, Meson, N-sphere, Nathan Rosen, Particle horizon, Partition function (statistical mechanics), Pöschl–Teller potential, Philip M. Morse, Poisson's equation, Polar coordinate system, Positronium, Quantization (physics), Quantum chromodynamics, Quantum electrodynamics, Quark, Romanovski polynomials, Schrödinger equation, ... Expand index (7 more) »
Quantum mechanical potentials

Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".

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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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Boltzmann constant

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

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Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

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Color confinement

In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 terakelvin (corresponding to energies of approximately 130–140 MeV per particle).

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Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group, known as the conformal group.

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Coupling constant

In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction.

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De Sitter invariant special relativity

In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space.

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Degrees of freedom (mechanics)

In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state.

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Dipole

In physics, a dipole is an electromagnetic phenomenon which occurs in two ways.

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Direct numerical simulation

A direct numerical simulation (DNS) is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model.

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Direct product

In mathematics, one can often define a direct product of objects already known, giving a new one.

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Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

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Electric dipole moment

The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system: that is, a measure of the system's overall polarity.

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Electric potential

Electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work/energy needed per unit of electric charge to move the charge from a reference point to a specific point in an electric field.

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Electromagnetism

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields.

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Electrostatics

Electrostatics is a branch of physics that studies slow-moving or stationary electric charges.

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Erwin Schrödinger

Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961), sometimes written as or, was a Nobel Prize–winning Austrian and naturalized Irish physicist who developed fundamental results in quantum theory.

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Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space.

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Ewald summation

Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems.

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Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases.

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Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations (Lie groups). Trigonometric Rosen–Morse potential and gauge theory are mathematical physics.

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Gauss's law

In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations.

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Gegenbauer polynomials

In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval with respect to the weight function (1 − x2)α–1/2.

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Geodesic

In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold.

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Hadron

In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong interaction.

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Hadron spectroscopy

Hadron spectroscopy is the subfield of particle physics that studies the masses and decays of hadrons.

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Harmonic function

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f\colon U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, \frac + \frac + \cdots + \frac.

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Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen.

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Hyperboloid

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes.

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Laplace operator

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space.

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Laplace–Beltrami operator

In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds.

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Light cone

In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

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List of quantum-mechanical potentials

This is a list of potential energy functions that are frequently used in quantum mechanics and have any meaning. Trigonometric Rosen–Morse potential and list of quantum-mechanical potentials are quantum mechanical potentials.

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Meson

In particle physics, a meson is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction.

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N-sphere

In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer.

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Nathan Rosen

Nathan Rosen (נתן רוזן; March 22, 1909 – December 18, 1995) was an American and Israeli physicist noted for his study on the structure of the hydrogen molecule and his collaboration with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.

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Particle horizon

The particle horizon (also called the cosmological horizon, the comoving horizon (in Scott Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the universe.

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Partition function (statistical mechanics)

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium.

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Pöschl–Teller potential

In mathematical physics, a Pöschl–Teller potential, named after the physicists Herta Pöschl (credited as G. Pöschl) and Edward Teller, is a special class of potentials for which the one-dimensional Schrödinger equation can be solved in terms of special functions. Trigonometric Rosen–Morse potential and Pöschl–Teller potential are mathematical physics and quantum mechanical potentials.

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Philip M. Morse

Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II.

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Poisson's equation

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. Trigonometric Rosen–Morse potential and Poisson's equation are mathematical physics.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Positronium

Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium.

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Quantization (physics)

Quantisation (in American English quantization) is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. Trigonometric Rosen–Morse potential and quantization (physics) are mathematical physics.

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Quantum chromodynamics

In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons.

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Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.

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Quark

A quark is a type of elementary particle and a fundamental constituent of matter.

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Romanovski polynomials

In mathematics, the Romanovski polynomials are one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics.

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Schrödinger equation

The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Trigonometric Rosen–Morse potential and Schrödinger equation are mathematical physics.

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Strong interaction

In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is a fundamental interaction that confines quarks into protons, neutrons, and other hadron particles.

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Superposition principle

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. Trigonometric Rosen–Morse potential and superposition principle are mathematical physics.

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References

[1] https://en.wikipedia.org/wiki/Trigonometric_Rosen–Morse_potential

, Strong interaction, Superposition principle, Surface (mathematics), Thermodynamic beta, Trigonometric functions, Wave equation, Wave function.

Trigonometric Rosen–Morse potential, the Glossary

Table of Contents

See also

Quantum mechanical potentials

References