Morse potential

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1: 12.17 Physical Applications

… ►See Buchholz (1969, §4) and Morse and Feshbach (1953a, pp. 515 and 553). … ►For this topic and other boundary-value problems see Boyd (1973), Hillion (1997), Magnus (1941), Morse and Feshbach (1953a, b), Müller (1988), Ott (1985), Rice (1954), and Shanmugam (1978). ►Lastly, parabolic cylinder functions arise in the description of ultra cold atoms in harmonic trapping potentials; see Busch et al. (1998) and Edwards et al. (1999).

2: 18.39 Applications in the Physical Sciences

… ►argument b) The Morse Oscillator …The finite system of functions ${\psi }_n$ is orthonormal in $L^2(ℝ,dx)$, see (18.34.7_3). …The corresponding eigenfunction transform is a generalization of the Kontorovich–Lebedev transform §10.43(v), see Faraut (1982, §IV). ►c) A Rational SUSY Potential argument ►The Schrödinger equation with potential …

3: Bibliography N

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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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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§13.28(i).

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Eigenstates, coherent states, and uncertainty products for the Morse oscillator. Phys. Rev. A (3) 19 (2), pp. 438–444.

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External Links:

ISSN 1050-2947, Document, Link, MathReview Entry

Referenced by:

(18.39.17), (18.39.18).

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4: 15.18 Physical Applications

… ►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

5: 17.17 Physical Applications

… ►See Kassel (1995). … ►It involves $q$-generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials. …

6: Bibliography S

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Resonances in $n$-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory. Ann. of Math. (2) 97, pp. 247–274.

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External Links:

ISSN 0003-486X, Document, Link, MathReview (K. Kumar)

Referenced by:

§1.18(viii).

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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External Links:

MathReview (R. Shail), ZentralBlatt

Referenced by:

§10.22(iv).

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Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory. National Bureau of Standards Applied Mathematics Series, No. 19, U. S. Government Printing Office, Washington, D.C..

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.23(iv), Ch.14, §31.3(iii).

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Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.

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External Links:

MathReview (H. Bateman), ZentralBlatt

Referenced by:

§28.1, 7th item, Notations S, Notations S.

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Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients. Technology Press of M. I. T. and John Wiley & Sons, Inc., New York.

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External Links:

ISBN 0262190028, 0262692910, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

1st item, Ch.30.

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7: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►At positive energies $E>0$, $\rho \ge 0$, and: … ► $R_{\mathrm{\infty }}=m_{\mathrm{e}}c{\alpha }^2/(2\mathrm{\hslash })$. … ►Both variable sets may be used for attractive and repulsive potentials: the $(ϵ,r)$ set cannot be used for a zero potential because this would imply $r=0$ for all $s$, and the $(\eta ,\rho )$ set cannot be used for zero energy $E$ because this would imply $\rho =0$ always. … ►

§33.22(vi) Solutions Inside the Turning Point

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8: Bibliography M

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Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions. Comput. Phys. Comm. 178 (7), pp. 535–551.

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External Links:

ISSN 0010-4655, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§15.19(i), §15.19(i).

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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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ISSN 0031-899X, ZentralBlatt

Referenced by:

(18.39.16).

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Methods of Theoretical Physics. Vol. 1, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§1.17(iii), §1.5(ii), §12.17, §12.17, §12.17.

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Methods of Theoretical Physics. Vol. 2, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Feshbach Publishing, http://www.feshbachpublishing.com/.

External Links:

Feshbach Publishing, MathReview (M. Pinl), ZentralBlatt

Referenced by:

§12.17, §12.17.

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9: 14.31 Other Applications

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§14.31(ii) Conical Functions

… ►These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). …

10: Bibliography Q

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Higher-Order SUSY, Exactly Solvable Potentials, and Exceptional Orthogonal Polynomials. Modern Physics Letters A 26, pp. 1843–1852.

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External Links:

Document, Link

Referenced by:

§18.38(iii).

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