quantum%20mechanics
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1: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Confluent hypergeometric equations and related solvable potentials in quantum mechanics.
J. Math. Phys. 41 (12), pp. 7964–7996.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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2: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Supersymmetry and quantum mechanics.
Phys. Rep. 251, pp. 267–385.
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Quasinormal modes of the extremal BTZ black hole.
Classical Quantum Gravity 21 (12), pp. 2801–2809.
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Schrödinger Operators, with Applications to Quantum Mechanics and Global Geometry.
Springer Verlag, New York.
3: Bibliography D
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The constrained quantum mechanical harmonic oscillator.
Proc. Cambridge Philos. Soc. 62, pp. 277–286.
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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2.
American Mathematical Society, Providence, RI.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Hydrodynamic Stability.
Cambridge University Press, Cambridge.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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4: Bibliography S
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Exact recursive evaluation of - and -coefficients for quantum-mechanical coupling of angular momenta.
J. Mathematical Phys. 16 (10), pp. 1961–1970.
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Semiclassical approximations to - and -coefficients for quantum-mechanical coupling of angular momenta.
J. Mathematical Phys. 16 (10), pp. 1971–1988.
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General relativity and quantum mechanics: towards a generalization of the Lambert function: a generalization of the Lambert function.
Appl. Algebra Engrg. Comm. Comput. 17 (1), pp. 41–47.
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The Gaussian Function in Calculations of Statistical Mechanics and Quantum Mechanics.
In Methods in Computational Physics: Advances in Research and Applications, B. Alder, S. Fernbach, and M. Rotenberg (Eds.),
Vol. 2, pp. 1–45.
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Spectral Methods in Chemistry and Physics. Applications to Kinetic Theory and Quantum Mechanics.
Scientific Computation, Springer-Verlag, Dordrecht.
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5: Bibliography M
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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Spin Systems, Statistical Mechanics and Painlevé Functions.
In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.),
NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 377–391.
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Quantum Mechanics. Vol. I.
North-Holland Publishing Co., Amsterdam.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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Diatomic molecules according to the wave mechanics. II: Vibrational levels.
Phys. Rev., II. Ser. 34, pp. 57–64.
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6: Bibliography L
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Quantum Mechanics: Non-relativistic Theory.
Pergamon Press Ltd., Oxford.
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Fluid Mechanics.
2nd edition, Pergamon Press, London.
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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics.
J. Math. Phys. 27 (5), pp. 1238–1265.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions.
third edition, Springer, New York.
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7: Bibliography B
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Moment equations for probability distributions in classical and quantum mechanics.
Phys. Rev. A 58 (3), pp. 1799–1809.
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Exactly Solved Models in Statistical Mechanics.
Academic Press Inc., London-New York.
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Quantum mechanics of one- and two-electron atoms.
Springer-Verlag, Berlin.
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Quantum Mechanics of One- and Two-electron Atoms.
Rosetta edition, Plenum Publishing Corp., New York.
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Angular Momentum in Quantum Physics: Theory and Application.
Encyclopedia of Mathematics and its Applications, Vol. 8, Addison-Wesley Publishing Co., Reading, M.A..
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8: Bibliography G
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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
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Error bounds in equilibrium statistical mechanics.
J. Math. Phys. 9, pp. 655–663.
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Quantum mechanics: fundamentals.
Second edition, Springer-Verlag, New York.
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General form of the quantum-defect theory.
Phys. Rev. A 19 (4), pp. 1485–1509.
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Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics.
Texts and Monographs in Physics, Springer.
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9: Bibliography P
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Introduction to quantum mechanics.
Dover Publications, Inc., New York.
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Ideas of Quantum Chemistry.
second edition, Elsevier, Amsterdam-New York.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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10: 10.73 Physical Applications
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►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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►In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential.
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