# q-deformed quantum mechanical

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## 1—10 of 59 matching pages

##### 1: 17.17 Physical Applications

###### §17.17 Physical Applications

… ►Quantum groups also apply $q$-series extensively. …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. …##### 2: 36.14 Other Physical Applications

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###### §36.14(iii) Quantum Mechanics

►Diffraction catastrophes describe the “semiclassical” connections between classical orbits and quantum wavefunctions, for integrable (non-chaotic) systems. …##### 3: 11.12 Physical Applications

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►More recently Struve functions have appeared in many particle quantum dynamical studies of spin decoherence (Shao and Hänggi (1998)) and nanotubes (Pedersen (2003)).

##### 4: 8.24 Physical Applications

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###### §8.24(i) Incomplete Gamma Functions

… ►###### §8.24(ii) Incomplete Beta Functions

►The function ${I}_{x}(a,b)$ appears in: Monte Carlo sampling in statistical mechanics (Kofke (2004)); analysis of packings of soft or granular objects (Prellberg and Owczarek (1995)); growth formulas in cosmology (Hamilton (2001)). ►###### §8.24(iii) Generalized Exponential Integral

… ►With more general values of $p$, ${E}_{p}\left(x\right)$ supplies fundamental auxiliary functions that are used in the computation of molecular electronic integrals in quantum chemistry (Harris (2002), Shavitt (1963)), and also wave acoustics of overlapping sound beams (Ding (2000)).##### 5: 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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##### 6: Vadim B. Kuznetsov

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►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics.
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##### 7: 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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##### 8: 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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##### 9: 18.39 Physical Applications

##### 10: 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 KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics.
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►An example from quantum mechanics is given in Landau and Lifshitz (1965), in which the exact solution of the Schrödinger equation for the motion of a particle in a homogeneous external field is expressed in terms of $\mathrm{Ai}\left(x\right)$.
…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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