in one and two dimensions

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1: Bibliography P

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Remarks on computing the probability integral in one and two dimensions. In Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, 1945, 1946, pp. 63–78.

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External Links:

MathReview (L. A. Aroian), ZentralBlatt

Referenced by:

(7.8.8), §7.8, Erratum (V1.0.17) for Equation (7.8.8).

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2: 1.6 Vectors and Vector-Valued Functions

… ►In either case … ►The geometrical image $C$ of a path $𝐜$ is called a simple closed curve if $𝐜$ is one-to-one, with the exception $𝐜(a)=𝐜(b)$. … ►

Green’s Theorem

… ►otherwise, one is the negative of the other. … ►

Green’s Theorem (for Volume)

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3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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Example 1: In one and two dimensions any $q(x)$ with a ‘Dip, or Well’ has a partly discrete spectrum

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4: Bibliography S

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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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External Links:

Document, MathReview Entry

Referenced by:

§1.18(viii).

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5: Bibliography C

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Bound states in one and two spatial dimensions. J. Math. Phys. 44 (2), pp. 406–422.

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External Links:

ISSN 0022-2488, Document, Link, MathReview (Pavel B. Kurasov)

Referenced by:

§1.18(viii).

Encodings:

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6: 37.2 General Orthogonal Polynomials of Two Variables

… ►In this section polynomials will be polynomials of two variables with real coefficients. …Then …Then $dim{𝒱}_n=n+1$. … ►One of the OPs resulting from this classification are the Hahn polynomials of two variables, see §37.10(iv).

7: 37.13 General Orthogonal Polynomials of $d$ Variables

… ►Basic definitions and properties of OPs of $d$ variables are similar to those of two variables in §37.2. … ►Analogous to the Krall–Sheffer classification in the two-variable case (see §37.2(viii)), one can ask for admissible $d$-variable second order PDOs $L$, i. … ►

In (37.14.11) on the simplex ${\mathrm{△}}^d$.

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In (37.15.16) on the ball ${𝔹}^d$.

… ►The corresponding OPs are products of one-variable OPs of Hahn class, as defined in §18.19. …

8: null

error generating summary

9: 22.19 Physical Applications

… ►With appropriate scalings, Newton’s equation of motion for a pendulum with a mass in a gravitational field constrained to move in a vertical plane at a fixed distance from a fulcrum is … ►Classical motion in one dimension is described by Newton’s equation … ►Two types of oscillatory motion are possible. For an initial displacement with , bounded oscillations take place near one of the two points of stable equilibrium $x=\pm \sqrt{1/\beta }$. … ►Whittaker (1964, Chapter IV) enumerates the complete class of one-body classical mechanical problems that are solvable this way. …

10: Bibliography B

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Quantum mechanics of one- and two-electron atoms. Springer-Verlag, Berlin.

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External Links:

MathReview (L. Van Hove), ZentralBlatt

Referenced by:

§18.39(ii), §18.39(ii).

Encodings:

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Quantum Mechanics of One- and Two-electron Atoms. Rosetta edition, Plenum Publishing Corp., New York.

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Notes:

Reprint (with corrections) of the original edition published in 1957 by Springer and Academic Press

External Links:

MathReview, ZentralBlatt (D. Geissler)

Referenced by:

§1.18(viii), §33.22(ii), §33.22(ii), §33.22(v).

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One- and two-electron photoejection from ${\mathrm{H}}^{-}$: A multichannel $J$-matrix calculation. Phys. Rev. A 14, pp. 2159–2173.

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External Links:

Document, Link

Referenced by:

§18.39(iv).

Encodings:

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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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External Links:

Document

Referenced by:

§1.18(viii).

Encodings:

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Two cold atoms in a harmonic trap. Found. Phys. 28 (4), pp. 549–559.

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External Links:

Document

Referenced by:

§12.17.

Encodings:

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