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1: 26.20 Physical Applications

… ►The latter reference also describes chemical applications of other combinatorial techniques. ►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). For an application of statistical mechanics to combinatorics, see Bressoud (1999). ►Other applications to problems in engineering, crystallography, biology, and computer science can be found in Beckenbach (1981) and Graham et al. (1995).

2: Tom M. Apostol

… ►He received his bachelor of science in chemical engineering in 1944 and a master’s degree in mathematics in 1946, both from the University of Washington, Seattle. … ►He was also a coauthor of three textbooks written to accompany the physics telecourse The Mechanical Universe …and Beyond. …

3: Mark J. Ablowitz

… ►He has a BS from the University of Rochester in Mechanical Engineering and a Ph. …

4: 17.17 Physical Applications

§17.17 Physical Applications

►In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. … ►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. See Kassel (1995). ►A substantial literature on $q$-deformed quantum-mechanical Schrödinger equations has developed recently. …

5: 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)). … ►Legendre functions $P_{\nu }\left(x\right)$ of complex degree $\nu$ appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …

6: Ranjan Roy

… ►(1974) degrees in mathematics from the Indian Institute of Technology Kharagpur, Indian Institute of Technology Kanpur, and the State University of New York at Stony Brook, respectively. … ►Roy has published many papers on differential equations, fluid mechanics, special functions, Fuchsian groups, and the history of mathematics. …

7: 22.18 Mathematical Applications

… ►Bowman (1953, Chapters V–VI) gives an overview of the use of Jacobian elliptic functions in conformal maps for engineering applications. … ►See Baxter (1982, p. 471) for an example from statistical mechanics. … … ►Algebraic curves of the form $y^2=P(x)$, where $P$ is a nonsingular polynomial of degree 3 or 4 (see McKean and Moll (1999, §1.10)), are elliptic curves, which are also considered in §23.20(ii). …

8: Brian Antonishek

… ►Antonishek received the Bachelor of Science degree in computer science from the University of Pittsburgh, Johnstown, Pennsylvania, in 1990 and the Master of Science degree in computer science from the University of Pittsburgh, Pittsburgh, Pennsylvania, in 1996. Before coming to NIST in 1997, he developed user interaction and scientific visualization techniques for viewing and analyzing 3D engineering data. …

9: Abdou Youssef

… ►He is also the inventor and architect of the mathematical search engine for the DLMF website. … ►degree in mathematics from the Lebanese University, and his M. …degrees in computer science from Princeton University. …

10: 36.14 Other Physical Applications

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§36.14(iii) Quantum Mechanics

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