quartic oscillator

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21: 28.33 Physical Applications

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Jager (1997, 1998) for relativistic oscillators.

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22: 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. …

23: Bibliography J

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Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste. Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).

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Notes:

Translated title: Mathieu functions and eigenfunctions of the relativistic oscillator.

External Links:

ISSN 0240-2963, Pdf, MathReview (Jean-Michel Ghez), ZentralBlatt

Referenced by:

7th item.

Encodings:

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24: 12.14 The Function $W(a,x)$

… ►For real $\mu$ and $t$ oscillations occur outside the $t$-interval $[-1,1]$. … ►In this case there are no real turning points, and the solutions of (12.2.3), with $z$ replaced by $x$, oscillate on the entire real $x$-axis. …

25: Bibliography D

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The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.

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External Links:

Document, MathReview (T. Erber)

Referenced by:

§12.11(i), §12.11(i), §12.17.

Encodings:

BibTeX

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26: 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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External Links:

ISSN 1751-8113, Document, Link, MathReview (Brian Simanek)

Referenced by:

§18.36(vi), §18.36(vi).

Encodings:

BibTeX

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27: Bibliography L

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Integrating some infinite oscillating tails. J. Comput. Appl. Math. 12/13, pp. 109–117.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§3.5(vii).

Encodings:

BibTeX

28: 19.2 Definitions

… ►Let $s^2(t)$ be a cubic or quartic polynomial in $t$ with simple zeros, and let $r(s,t)$ be a rational function of $s$ and $t$ containing at least one odd power of $s$. …

29: 32.11 Asymptotic Approximations for Real Variables

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If , then $w(x)$ oscillates about, and is asymptotic to, $-\sqrt{\frac{1}{6}|x|}$ as $x\to -\mathrm{\infty }$.

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30: Bibliography S

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

Encodings:

BibTeX

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