bound-state problems
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7 matching pages
1: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►For scattering problems, the interior solution is then matched to a linear combination of a pair of Coulomb functions, and , or and , to determine the scattering -matrix and also the correct normalization of the interior wave solutions; see Bloch et al. (1951).
►For bound-state problems only the exponentially decaying solution is required, usually taken to be the Whittaker function .
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2: 18.39 Applications in the Physical Sciences
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►Bound state solutions to the relativistic Dirac Equation, for this same problem of a single electron attracted by a nucleus with protons, involve Laguerre polynomials of fractional index.
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3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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Bounded and Unbounded Linear Operators
… ►, of unit multiplicity, unless otherwise stated. … ►The bound states are in the negative energy discrete spectrum, and the scattering states are in the positive energy continuous spectrum, , or, said more simply, in the continuum. … … ►If is a bounded operator then its spectrum is a closed bounded subset of . …4: Bibliography G
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Quasirandom distributed bases for bound problems.
J. Chem. Phys. 114 (9), pp. 3929–3939.
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Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
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Error bounds in equilibrium statistical mechanics.
J. Math. Phys. 9, pp. 655–663.
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New method for constructing wavefunctions for bound states and scattering.
J. Chem. Phys. 51, pp. 14–25.
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Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
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5: Bibliography L
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Bounds for modified Bessel functions.
J. Comput. Appl. Math. 34 (3), pp. 263–267.
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Bessel functions: Monotonicity and bounds.
J. London Math. Soc. (2) 61 (1), pp. 197–215.
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Problems of Mathematical Physics.
Revised, enlarged and corrected English edition; translated
and edited by Richard A. Silverman. With a supplement by
Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..
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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Comput. Phys. Comm. 99 (2-3), pp. 297–306.
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Statistical Physics, Part 2: Theory of the Condensed State.
Pergamon Press, Oxford.
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6: Bibliography B
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Coefficient functions for an inhomogeneous turning-point problem.
Mathematika 38 (2), pp. 217–238.
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New “coherent” states associated with non-compact groups.
Comm. Math. Phys. 21 (1), pp. 41–55.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Criterion for Existence of a Bound State In One Dimension.
American Journal of Physics 68 (2), pp. 160–161.
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7: Bibliography S
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Lamé polynomial solutions to some elliptic crack and punch problems.
Internat. J. Engrg. Sci. 16 (8), pp. 551–563.
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The Problem of Moments.
4th edition, American Mathematical Society Mathematical Surveys, Vol. 1, American Mathematical Society, Providence, RI.
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The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions.
Annals of Physics 97 (2), pp. 279–288.
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Some Boundary Value Problems Associated with the Heun Equation.
Ph.D. Thesis, London University.
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Mixed Boundary Value Problems in Potential Theory.
North-Holland Publishing Co., Amsterdam.
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