q-deformed quantum mechanical
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11: 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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12: 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)). …13: 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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14: 5.20 Physical Applications
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Rutherford Scattering
►In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift ; see (33.2.10) and Clark (1979). ►Solvable Models of Statistical Mechanics
…15: 28.33 Physical Applications
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Meixner and Schäfke (1954, §§4.1, 4.2, and 4.7) for quantum mechanical problems and rotation of molecules.
Fukui and Horiguchi (1992) for quantum theory.
16: 12.17 Physical Applications
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►Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator.
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17: 18.39 Applications in the Physical Sciences
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§18.39(i) Quantum Mechanics
… ►Introduction and One-Dimensional (1D) Systems
… ►1D Quantum Systems with Analytically Known Stationary States
… ►c) A Rational SUSY Potential … ►§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom
…18: 23.21 Physical Applications
19: 25.17 Physical Applications
§25.17 Physical Applications
►Analogies exist between the distribution of the zeros of on the critical line and of semiclassical quantum eigenvalues. …See Armitage (1989), Berry and Keating (1998, 1999), Keating (1993, 1999), and Sarnak (1999). ►The zeta function arises in the calculation of the partition function of ideal quantum gases (both Bose–Einstein and Fermi–Dirac cases), and it determines the critical gas temperature and density for the Bose–Einstein condensation phase transition in a dilute gas (Lifshitz and Pitaevskiĭ (1980)). 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). …20: 32.16 Physical Applications
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