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...ated to [[angular momentum coupling|recoupling coefficients]] in [[quantum mechanics]] involving four angular momenta ...e matrix elements are independent of the total angular momentum projection quantum number (<math>m_9</math>): ...

...her enter in the quantum mechanics of the [[Morse potential]] and of the [[Quantum harmonic oscillator#Example: 3D isotropic harmonic oscillator|3D isotropic The following integral is needed in the quantum mechanical treatment of the [[Hydrogen atom#Wavefunction|hydrogen atom]], ...

...armonic potentials.<ref>H. J. W. Müller-Kirsten, ''Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral'', 2nd ed. World Scientific, 2012, |title = Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral, 2nd ed. ...

...the geometry of a tetrahedron. If the 6-''j'' symbol is determined by the quantum numbers ''j''₁, ..., ''j''₆ the associated tetrahedro ...s ''V''_i, ''V''_j, ''V''_k of a group (or [[quantum group]]), one has a natural isomorphism ...

In [[quantum mechanics]], the '''Wigner 3-j symbols''', also called 3''-jm'' symbols, are an alter The ''j'' and ''m'' components are angular-momentum quantum numbers, i.e., every {{math|''j''}} (and every corresponding {{math|''m''}} ...

...ons in many fields of the physical sciences, such as [[optics]], [[quantum mechanics]], and [[general relativity]]. They tend to occur in problems involving per ...ed with boundary conditions<ref>Dingle and Müller (1962)</ref> (in quantum mechanics this provides the splitting of the eigenvalues into energy bands).<ref>Müll ...

This equation arises in quantum mechanics, in the radial part of the solution of the [[Schrödinger equation]] for a o In quantum mechanics, they are the solutions of Schrödinger's equation for the harmonic oscillat ...

* in [[physics]], where they give rise to the [[eigenstate]]s of the [[quantum harmonic oscillator]]; This expansion is needed to resolve the [[wavefunction]] of a [[quantum harmonic oscillator]] such that it agrees with the classical approximation ...

...ted that the Lambert {{mvar|W}} function provides an exact solution to the quantum-mechanical [[Delta potential#Double delta potential|double-well Dirac delta The Lambert {{mvar|W}} function appears in a quantum-mechanical potential, which affords the fifth – next to those of the harmon ...

...r are needed. For this we have Gaunt's formula <ref>From John C. Slater ''Quantum Theory of Atomic Structure'', McGraw-Hill (New York, 1960), Volume I, page * {{citation|first=A.R.|last=Edmonds|title=Angular Momentum in Quantum Mechanics|year=1957|publisher=Princeton University Press|isbn=978-0-691-07912-7|url-a ...

.../''x'')^{{{pipe}}''α''{{pipe}}}}} otherwise.<ref>{{cite book|title=Quantum Electrodynamics |last1=Greiner |first1=Walter |last2=Reinhardt |first2=Joac ...ndrical infinite potential barrier.<ref>Griffiths. Introduction to Quantum Mechanics, 2nd edition, p.&nbsp;154.</ref> This differential equation, and the Riccat ...

...formal derivation of the Legendre polynomial in the context of the quantum mechanics of hydrogen] ...

...gnores losses due to [[electromagnetic radiation]] and [[quantum mechanics|quantum effects]], which become significant when the particles are moving at high s ...ions; of a mass attached to a fixed point by a perfectly elastic [[spring (mechanics)|spring]]; or of any object that moves under influence of an attractive for ...