# Category: Quantum models

Quantum LC circuit
An LC circuit can be quantized using the same methods as for the quantum harmonic oscillator. An LC circuit is a variety of resonant circuit, and consists of an inductor, represented by the letter L,
Quantum harmonic oscillator
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
Dihydrogen cation
The dihydrogen cation or hydrogen molecular ion is a cation (positive ion) with formula H+2. It consists of two hydrogen nuclei (protons) sharing a single electron. It is the simplest molecular ion. T
Transverse-field Ising model
The transverse field Ising model is a quantum version of the classical Ising model. It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin proj
Two-electron atom
In atomic physics, a two-electron atom or helium-like ion is a quantum mechanical system consisting of one nucleus with a charge of Ze and just two electrons. This is the first case of many-electron s
Quantum capacitance
Quantum capacitance, also called chemical capacitance and electrochemical capacitance , is a quantity first introduced by Serge Luryi (1988), and is defined as the variation of electrical charge with
Spin-1/2
In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1/2. The spin number describes how ma
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 e
1s Slater-type function
A normalized 1s Slater-type function is a function which is used in the descriptions of atoms and in a broader way in the description of atoms in molecules. It is particularly important as the accurat
Rigid rotor
In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three a
Two-state quantum system
In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum stat
Hooke's atom
Hooke's atom, also known as harmonium or hookium, refers to an artificial helium-like atom where the Coulombic electron-nucleus interaction potential is replaced by a harmonic potential. This system i
Fermi gas
An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in g
Hydrodynamic quantum analogs
The hydrodynamic quantum analogs refer to experimentally observed phenomena involving bouncing fluid droplets over a vibrating fluid bath that behave analogously to several quantum mechanical systems.
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by
Particle in a ring
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, who
Spherium
The "spherium" model consists of two electrons trapped on the surface of a sphere of radius . It has been used by Berry and collaborators to understand both weakly and strongly correlated systems and
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 to where it cannot escape, because the po
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
Adiabatic quantum motor
An adiabatic quantum motor is a mechanical device, typically nanometric, driven by a flux of quantum particles and able to perform cyclic motions. The adjective “adiabatic” in this context refers to t
Solution of Schrödinger equation for a 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 th
Dirac membrane
In quantum mechanics, a Dirac membrane is a model of a charged membrane introduced by Paul Dirac in 1962. Dirac's original motivation was to explain the mass of the muon as an excitation of the ground
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 Sc
Free electron model
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who
Empty lattice approximation
The empty lattice approximation is a theoretical electronic band structure model in which the potential is periodic and weak (close to constant). One may also consider an empty irregular lattice, in w
Spin quantum number
In atomic physics, the spin quantum number is a quantum number (designated ms) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particl
Morse potential
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibratio
List of quantum-mechanical systems with analytical solutions
Much insight in quantum mechanics can be gained from understanding the closed-form solutions to the time-dependent non-relativistic Schrödinger equation. It takes the form where is the wave function o
Helium atom
A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with either one or two neutron
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
Particle in a one-dimensional lattice
In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the cr
Quantum pendulum
The quantum pendulum is fundamental in understanding hindered internal rotations in chemistry, quantum features of scattering atoms, as well as numerous other quantum phenomena. Though a pendulum not
Free particle
In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means th
Particle in a spherically symmetric potential
In the quantum mechanics description of a particle in spherical coordinates, a spherically symmetric potential, is a potential that depends only on the distance between the particle and a defined cent