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q-deformed quantum mechanical

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11: 13.28 Physical Applications
For potentials in quantum mechanics that are solvable in terms of confluent hypergeometric functions see Negro et al. (2000). …
12: 14.31 Other Applications
§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
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. …
14: 5.20 Physical Applications
Rutherford Scattering
In nonrelativistic quantum mechanics, collisions between two charged particles are described with the aid of the Coulomb phase shift ph Γ ( + 1 + i η ) ; see (33.2.10) and Clark (1979).
Solvable Models of Statistical Mechanics
15: 28.33 Physical Applications
  • Meixner and Schäfke (1954, §§4.1, 4.2, and 4.7) for quantum mechanical problems and rotation of molecules.

  • Hunter and Kuriyan (1976) and Rushchitsky and Rushchitska (2000) for wave mechanics.

  • Fukui and Horiguchi (1992) for quantum theory.

  • 16: 12.17 Physical Applications
    Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator. …
    17: 18.39 Applications in the Physical Sciences
    §18.39(i) Quantum Mechanics
    Introduction and One-Dimensional (1D) Systems
    1D Quantum Systems with Analytically Known Stationary States
    c) A Rational SUSY Potential argument
    §18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom
    18: 23.21 Physical Applications
    §23.21 Physical Applications
  • Quantum field theory. See Witten (1987).

  • Statistical mechanics. See Baxter (1982, p. 434) and Itzykson and Drouffe (1989, §9.3).

  • 19: 25.17 Physical Applications
    §25.17 Physical Applications
    Analogies exist between the distribution of the zeros of ζ ( s ) 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
    Statistical Physics
    Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. … For the Ising model see Barouch et al. (1973), Wu et al. (1976), and McCoy et al. (1977). For applications in 2D quantum gravity and related aspects of the enumerative topology see Di Francesco et al. (1995). …