solution of a rational Schrödinger equation

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1: 18.39 Applications in the Physical Sciences

… ►c) A Rational SUSY Potential argument …

2: 18.36 Miscellaneous Polynomials

… ►In §18.39(i) it is seen that the functions, $\sqrt{w(x)}{\widehat{H}}_{n+3}\left(x\right)$, are solutions of a Schrödinger equation with a rational potential energy; and, in spite of first appearances, the Sturm oscillation theorem, Simon (2005c, Theorem 3.3, p. 35), is satisfied. …

3: 18.38 Mathematical Applications

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Differential Equations: Spectral Methods

… ►Schneider et al. (2016) discuss DVR/Finite Element solutions of the time-dependent Schrödinger equation. … ►The solved Schrödinger equations of §18.39(i) involve shape invariant potentials, and thus are in the family of supersymmetric or SUSY potentials. … ►Hermite EOP’s appear in solutions of a rationally modified Schrödinger equation in §18.39. … ►EOP’s are the subject of recent work on rational solutions to the fourth Painlevé equation, see Clarkson (2003a) and Marquette and Quesne (2016),where use of Hermite EOP’s makes a connection to quantum mechanics. …

4: Bibliography S

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Rational surfaces associated with affine root systems and geometry of the Painlevé equations. Comm. Math. Phys. 220 (1), pp. 165–229.

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External Links:

ISSN 0010-3616, Document, MathReview (I. Dolgachev), ZentralBlatt

Referenced by:

§32.7(viii).

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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations. SIAM J. Math. Anal. 10 (4), pp. 823–838.

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External Links:

ISSN 0036-1410, Document, MathReview (Ernest G. Kalnins), ZentralBlatt

Referenced by:

§28.32(i).

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcendent. Phys. D 3 (1-2), pp. 165–184.

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External Links:

Document, ZentralBlatt

Referenced by:

§32.11(ii).

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Asymptotic Solutions of the One-dimensional Schrödinger Equation. American Mathematical Society, Providence, RI.

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Notes:

Translated from the 1990 Russian original by Vadim Khidekel

External Links:

ISBN 0-8218-0563-3, MathReview (Denise Huet), ZentralBlatt

Referenced by:

§31.13.

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The linear differential equation whose solutions are the products of solutions of two given differential equations. J. Math. Anal. Appl. 98 (1), pp. 130–147.

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External Links:

ISSN 0022-247X, Document, FullText, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§1.13(v).

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