This is a list of

potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...

functions that are frequently used in

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

and have any meaning.

One-dimensional potentials

Rectangular potential barrier In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. ...

Delta potential In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds to a potential which is zero everywhere, except at a single point, where it t ...

(aka "contact potential") * Double delta potential *

Step potential In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a ...

* Periodic potential * Barrier potential * Gaussian potential * Eckart potential

Wells

Quantum well A quantum well is a potential well with only discrete energy values. The classic model used to demonstrate a quantum well is to confine particles, which were initially free to move in three dimensions, to two dimensions, by forcing them to occup ...

Potential well A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is cap ...

Finite potential well The finite potential well (also known as the finite square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which a particle is confined to a "box", but one which has finite potential "walls". Unlike ...

Infinite potential well In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes the movement of a free particle in a small space surrounded by impenetrable barriers. The model is mainly used a ...

Double-well potential The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it ...

Semicircular potential well In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The particle follows the path of a semicircle from 0 to \pi where it cannot escape, because the potential from \pi to 2 \pi is infin ...

* Circular potential well * Spherical potential well *

Triangular potential well A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensiona ...

Interatomic potentials

Interatomic potential Interatomic potentials are mathematical functions to calculate the potential energy of a system of atoms with given positions in space.M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, England, 198 ...

Bond order potential Bond order potential is a class of empirical (analytical) interatomic potentials which is used in molecular dynamics and molecular statics simulations. Examples include the Tersoff potential, the EDIP potential, the Brenner potential, the Finnis� ...

* EAM potential *

Coulomb potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...

Buckingham potential In theoretical chemistry, the Buckingham potential is a formula proposed by Richard Buckingham which describes the Pauli exclusion principle and van der Waals energy \Phi_(r) for the interaction of two atoms that are not directly bonded as a funct ...

Lennard-Jones potential In computational chemistry, molecular physics, and physical chemistry, the Lennard-Jones potential (also termed the LJ potential or 12-6 potential; named for John Lennard-Jones) is an intermolecular pair potential. Out of all the intermolecul ...

Morse potential The Morse potential, named after physicist Philip M. Morse, is a convenient Interatomic potential, interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the oscillation, vibrational struct ...

Morse/Long-range potential The Morse/Long-range potential (MLR potential) is an interatomic interaction model for the potential energy of a diatomic molecule. Due to the simplicity of the regular Morse potential (it only has three adjustable parameters), it is very limit ...

* Rosen–Morse potential *

Trigonometric Rosen–Morse potential The trigonometric Rosen–Morse potential, named after the physicists Nathan Rosen and Philip M. Morse, is among the exactly solvable quantum mechanical potentials. Definition In dimensionless units and modulo additive constants, it is defined ...

Stockmayer potential The Stockmayer potential is a mathematical model for representing the interactions between pairs of atoms or molecules. It is defined as a Lennard-Jones potential with a point electric dipole moment The electric dipole moment is a measure of th ...

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 ter ...

Axilrod–Teller potential In molecular physics, the Axilrod–Teller potential (also known as the Axilrod–Teller–Muto or ATM potential) describes the interaction potential (energy) between three atoms, capturing effects beyond simple pairwise attractions. It builds on ...

Mie potential The Mie potential is an interaction potential describing the interactions between particles on the atomic level. It is mostly used for describing intermolecular interactions, but at times also for modeling intramolecular interaction, i.e. bonds. T ...

Oscillators

Harmonic potential The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, ...

(

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'': \vec F = -k \vec x, where ''k'' is a positive const ...

) *

( morse oscillator) *

( Morse/Long-range oscillator) * Kratzer potential ( Kratzer oscillator)

Quantum Field theory

Yukawa potential Yukawa (written: 湯川) is a Japanese surname, but is also applied to proper nouns. People * Diana Yukawa (born 1985), Anglo-Japanese solo violinist. She has had two solo albums with BMG Japan, one of which opened to #1 * Hideki Yukawa (1907–1 ...

Coleman–Weinberg potential The Coleman–Weinberg model represents quantum electrodynamics of a scalar field in four-dimensions. The Lagrangian for the model is :L = -\frac (F_)^2 + , D_ \phi, ^2 - m^2 , \phi, ^2 - \frac , \phi, ^4 where the scalar field is complex, F_=\p ...

* Uehling potential *

Woods–Saxon potential The Woods–Saxon potential is a mean field potential for the nucleons (protons and neutrons) inside the atomic nucleus, which is used to describe approximately the forces applied on each nucleon, in the nuclear shell model for the structure of th ...

Cornell potential In particle physics, the Cornell potential is an effective method to account for the confinement of quarks in quantum chromodynamics (QCD). It was developed by Estia J. Eichten, Kurt Gottfried, Toichiro Kinoshita, John Kogut, Kenneth Lane a ...

Miscellaneous

Quantum potential The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952. Initially presented under the name ''quantum-mechanical potential'', subsequently ''qu ...

Pseudopotential In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering. The pseudopotential approximation was first introduce ...

Superpotential In theoretical physics, the superpotential is a function in supersymmetric quantum mechanics. Given a superpotential, two "partner potentials" are derived that can each serve as a potential in the Schrödinger equation. The partner potentials hav ...

Komar superpotential In general relativity, the Komar superpotential, corresponding to the invariance of the Hilbert–Einstein Lagrangian \mathcal_\mathrm = R \sqrt \, \mathrm^4x, is the tensor density: : U^(,\xi) =\nabla^\xi^ = (g^ \nabla_\xi^ - g^ \nabla_\xi^) \, ...