Harmonic Oscillator

HermiteH   ▪ LaguerreL

Hydrogen Atom

SphericalHarmonicY   ▪ LaguerreL   ▪ Hypergeometric1F1   ▪ WhittakerM

Linear Potential

AiryAi   ▪ AiryAiPrime   ▪ AiryBi   ▪ AiryAiZero   ▪ AiryBiZero

Periodic Potential

MathieuS   ▪ MathieuC   ▪ MathieuCharacteristicExponent

Coulomb Potential

CoulombF   ▪ CoulombG   ▪ CoulombH1   ▪ CoulombH2

Spheroidal Geometries

SpheroidalPS   ▪ SpheroidalS1   ▪ SpheroidalEigenvalue

Scattering Theory

LegendreP   ▪ SphericalBesselJ   ▪ LegendreQ

Dirac Equation Solutions

Hypergeometric1F1   ▪ BesselK

Angular Momentum

ClebschGordan   ▪ ThreeJSymbol   ▪ SixJSymbol   ▪ JacobiP   ▪ PauliMatrix

Advanced Potentials

HeunG   ▪ HeunC   ▪ HeunD   ▪ HeunB   ▪ HeunT   ▪ HeunTPrime   ▪ Hypergeometric2F1

Related Tech Notes

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• Special Functions

Related Guides

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• Special Functions
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• Functions Used in Optics
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• Functions for Separable Coordinate Systems

Related Links

• Demonstrations related to Functions Used in Quantum Mechanics (Wolfram Demonstrations Project)