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- Dirac fermion
- Thirring model
- List of integrable models
- Arnold's cat map
- Bäcklund transform
- Baker's map
- Bethe ansatz
- Bogdanov map
- Boolean network
- Bretherton equation
- Bullough–Dodd model
- Chiral Potts curve
- Corner transfer matrix
- Domino tiling
- Dym equation
- Eight-vertex model
- Gingerbreadman map
- Hard hexagon model
- Ice-type model
- Inverse scattering transform
- Ising model
- Kadomtsev–Petviashvili equation
- KdV hierarchy
- Korteweg–de Vries equation
- Kramers–Wannier duality
- Kundu equation
- Kuramoto model
- Lax pair
- Minimal models
- Nonlinear partial differential equation
- Nonlinear Schrödinger equation
- Novikov–Veselov equation
- Potts model
- Quantum affine algebra
- Quantum inverse scattering method
- Riemann–Hilbert problem
- Rosenau–Hyman equation
- Schwinger model
- Sine-Gordon equation
- Spherical model
- Square-lattice Ising model
- Thirring–Wess model
- Toda field theory
- Toda lattice
- Topological quantum number
- Wess–Zumino–Witten model
- Yang–Baxter equation
- Yangian
- Z N model
- Quantum finite automata
- Automorphism
- Quantum convolutional code
- Simon's problem
- Hidden subgroup problem
- Entanglement-assisted stabilizer formalism
- Trapped ion quantum computer
- Earnshaw's theorem
- Transmon
- Quantum Fourier transform
- KLM protocol
- Quantum teleportation
- Boson sampling
- Creation and annihilation operators
- Airy function
- Affine q-Krawtchouk polynomials
- Al-Salam–Chihara polynomials
- Bateman function
- Bessel function
- Bessel polynomials
- Bessel–Clifford function
- Beta function
- Big q-Jacobi polynomials
- Big q-Laguerre polynomials
- Chebyshev polynomials
- Classical orthogonal polynomials
- Confluent hypergeometric function
- Continuous big q-Hermite polynomials
- Continuous dual Hahn polynomials
- Continuous dual q-Hahn polynomials
- Continuous Hahn polynomials
- Continuous q-Hahn polynomials
- Continuous q-Hermite polynomials
- Continuous q-Jacobi polynomials
- Continuous q-Laguerre polynomials
- Continuous q-Legendre polynomials
- Coulomb wave function
- Cunningham function
- Discrete q-Hermite polynomials
- Dual Hahn polynomials
- Dual q-Hahn polynomials
- Dual q-Krawtchouk polynomials
- Elliptic integral
- Error function
- Exponential function
- Exponential integral
- Fresnel integral
- Gamma function
- Gegenbauer polynomials
- Hahn polynomials
- Hermite polynomials
- Jacobi polynomials
- Kelvin functions
- Laguerre polynomials
- Legendre polynomials
- Little q-Jacobi polynomials
- Little q-Laguerre polynomials
- Logarithmic integral function
- Neumann function
- Parabolic cylinder function
- Q-Bessel polynomials
- Q-Charlier polynomials
- Q-Hahn polynomials
- Q-Krawtchouk polynomials
- Q-Laguerre polynomials
- Q-Meixner polynomials
- Q-Meixner–Pollaczek polynomials
- Q-Racah polynomials
- Quantum q-Krawtchouk polynomials
- Romanovski polynomials
- Solid harmonics
- Sonine formula
- Spherical harmonics
- Stieltjes–Wigert polynomials
- Table of spherical harmonics
- Toronto function
- Trigonometric integral
- Whittaker function
- Wigner D-matrix
- Zonal spherical harmonics