quantum wave-packets
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11: Simon Ruijsenaars
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►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas.
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12: 34.10 Zeros
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►In a symbol, if the three angular momenta do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the symbol is zero.
…However, the and symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled.
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13: Tom H. Koornwinder
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►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC.
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14: 6.17 Physical Applications
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►Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics.
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15: T. Mark Dunster
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►He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory.
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16: 31.17 Physical Applications
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§31.17(i) Addition of Three Quantum Spins
►The problem of adding three quantum spins , , and can be solved by the method of separation of variables, and the solution is given in terms of a product of two Heun functions. … ►§31.17(ii) Other Applications
►Heun functions appear in the theory of black holes (Kerr (1963), Teukolsky (1972), Chandrasekhar (1984), Suzuki et al. (1998), Kalnins et al. (2000)), lattice systems in statistical mechanics (Joyce (1973, 1994)), dislocation theory (Lay and Slavyanov (1999)), and solution of the Schrödinger equation of quantum mechanics (Bay et al. (1997), Tolstikhin and Matsuzawa (2001), and Hall et al. (2010)). … ►More applications—including those of generalized spheroidal wave functions and confluent Heun functions in mathematical physics, astrophysics, and the two-center problem in molecular quantum mechanics—can be found in Leaver (1986) and Slavyanov and Lay (2000, Chapter 4). …17: 9.16 Physical Applications
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►Airy functions are applied in many branches of both classical and quantum physics.
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►The frequent appearances of the Airy functions in both classical and quantum physics is associated with wave equations with turning points, for which asymptotic (WKBJ) solutions are exponential on one side and oscillatory on the other.
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►The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics.
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►This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point.
A study of the semiclassical description of quantum-mechanical scattering is given in Ford and Wheeler (1959a, b).
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18: 13.28 Physical Applications
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►For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000).
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19: 14.31 Other Applications
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§14.31(iii) Miscellaneous
►Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)). …20: Michael V. Berry
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►Berry has published numerous papers on theoretical physics, mainly in quantum mechanics and optics and including the development of associated mathematics, especially asymptotics and geometry.
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