Casimir–Polder effect
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1: 25.17 Physical Applications
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►See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999).
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►Quantum field theory often encounters formally divergent sums that need to be evaluated by a process of regularization: for example, the energy of the electromagnetic vacuum in a confined space (Casimir–Polder effect).
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2: 24.18 Physical Applications
§24.18 Physical Applications
►Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). …3: Sidebar 7.SB1: Diffraction from a Straightedge
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►The faint circular patterns are additional diffraction effects due to imperfections in the edge.
4: 15.18 Physical Applications
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►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)).
►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).
5: 18.38 Mathematical Applications
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►A further operator, the so-called Casimir operator
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6: 5.21 Methods of Computation
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►An effective way of computing in the right half-plane is backward recurrence, beginning with a value generated from the asymptotic expansion (5.11.3).
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7: 27.17 Other Applications
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►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
8: 7.21 Physical Applications
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►Voigt functions , , can be regarded as the convolution of a Gaussian and a Lorentzian, and appear when the analysis of light (or particulate) absorption (or emission) involves thermal motion effects.
…Dawson’s integral appears in de-convolving even more complex motional effects; see Pratt (2007).
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9: Daniel W. Lozier
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►Army Engineer Research and Development Laboratory in Virginia on finite-difference solutions of differential equations associated with nuclear weapons effects.
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10: About MathML
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►Most modern browsers support ‘Web Fonts’, fonts that are effectively included with a web site.
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