rotation%20group
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1: Philip J. Davis
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►Davis joined the Section as part of a distinguished group of researchers studying mathematical methods for exploiting the new computational power.
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►After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined.
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►DLMF users can rotate, rescale, zoom and otherwise explore mathematical function surfaces.
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2: 16.24 Physical Applications
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►The symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations.
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3: Bibliography K
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The group
, separation of variables and the hydrogen atom.
SIAM J. Appl. Math. 30 (4), pp. 630–664.
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Quantum Groups.
Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.
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Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups.
In Special Functions: Group Theoretical Aspects and Applications,
pp. 1–85.
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Compact quantum groups and -special functions.
In Representations of Lie Groups and Quantum Groups,
Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.
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Sur le problème de la rotation d’un corps solide autour d’un point fixe.
Acta Math. 12 (1), pp. 177–232 (French).
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4: Bibliography P
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds.
Springer-Verlag, New York.
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5: 29.18 Mathematical Applications
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§29.18(iv) Other Applications
… ►Patera and Winternitz (1973) finds bases for the rotation group.6: Bibliography T
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Fourier Analysis on Finite Groups and Applications.
London Mathematical Society Student Texts, Vol. 43, Cambridge University Press, Cambridge.
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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett. 29 (16), pp. 1114–1118.
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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
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Combinatorial Group Theory, Riemann Surfaces and Differential Equations.
In Contributions to Group Theory,
Contemp. Math., Vol. 33, pp. 467–519.
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7: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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New “coherent” states associated with non-compact groups.
Comm. Math. Phys. 21 (1), pp. 41–55.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Spectroscopy of Molecular Rotation in Gases and Liquids.
Cambridge University Press, Cambridge.
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8: 13.27 Mathematical Applications
§13.27 Mathematical Applications
►Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices. The elements of this group are of the form …The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions. … …9: 17.17 Physical Applications
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►See Berkovich and McCoy (1998) and Bethuel (1998) for recent surveys.
►Quantum groups also apply -series extensively.
Quantum groups are really not groups at all but certain Hopf algebras.
They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics.
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10: 15.17 Mathematical Applications
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