quantum probability distributions

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1: 24.18 Physical Applications

… ►Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). ►Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).

2: Bibliography B

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Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.

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§24.18.

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3: Bibliography H

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Computation of certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven 1968 (2), pp. 81–104. (errata insert) (Russian).

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External Links:

MathReview (H. A. Lauwerier)

Referenced by:

§7.14(iii).

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Certain integrals that contain a probability function and degenerate hypergeometric functions. Bul. Akad. S̆tiince RSS Moldoven 1969 (2), pp. 40–47 (Russian).

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MathReview (Wazir Hasan Abdi)

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§7.14(iii).

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Some integrals that contain a probability function and hypergeometric functions. Bul. Akad. Štiince RSS Moldoven 1970 (1), pp. 49–62 (Russian).

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MathReview (R. G. Langebartel)

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§7.14(iii).

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The Laplace transform for expressions that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).

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MathReview (L. Berg)

Referenced by:

§7.14(iii).

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Certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 86–88, 95 (Russian).

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MathReview (C. Tanaka)

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§7.14(iii).

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4: Bibliography P

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Handbook of the Normal Distribution. Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.

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Notes:

A revised and expanded 2nd edition was published in 1996.

External Links:

ISBN 0-8247-1541-1, MathReview (S. Kotz), ZentralBlatt

Referenced by:

§7.20(iii).

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Introduction to quantum mechanics. Dover Publications, Inc., New York.

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Notes:

With applications to chemistry, Reprint of the 1935 original

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ISBN 0-486-64871-0, MathReview Entry

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§1.18(v), §18.39(i), §18.39(ii), §18.39(ii).

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The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt

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§35.9.

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Ideas of Quantum Chemistry. second edition, Elsevier, Amsterdam-New York.

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ISBN 978-0-444-59436-5

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§18.39(ii).

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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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MathReview (L. A. Aroian), ZentralBlatt

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

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5: Bibliography L

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Quantum Mechanics: Non-relativistic Theory. Pergamon Press Ltd., Oxford.

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Notes:

Revised second edition. Course of Theoretical Physics, Vol. 3. Translated from the Russian by J. B. Sykes and J. S. Bell

External Links:

MathReview, ZentralBlatt

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§9.16.

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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics. J. Math. Phys. 27 (5), pp. 1238–1265.

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ISSN 0022-2488, Document, MathReview (Basilis C. Xanthopoulos), ZentralBlatt

Referenced by:

§30.12, §31.17(ii).

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On the Darling-Mandelbrot probability density and the zeros of some incomplete gamma functions. Constr. Approx. 10 (1), pp. 15–30.

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ISSN 0176-4276, Document, MathReview (P. Anandani), ZentralBlatt

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§8.13(i).

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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions. third edition, Springer, New York.

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ISBN 0387955518

Referenced by:

§18.39(iii).

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Sur la distribution des nombres premiers. Comptes Rendus de l’Academie des Sciences, Paris 158, pp. 1869–1872 (French).

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ZentralBlatt

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§27.12.

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6: Bibliography M

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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case. J. Multivariate Anal. 77 (1), pp. 21–53.

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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

Referenced by:

§35.9.

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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case. J. Multivariate Anal. 82 (2), pp. 299–330.

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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

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§35.9.

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The exponential integral distribution. Statist. Probab. Lett. 5 (3), pp. 209–211.

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ISSN 0167-7152, Document, MathReview Entry, ZentralBlatt

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§8.19(xi).

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Quantum Mechanics. Vol. I. North-Holland Publishing Co., Amsterdam.

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Notes:

Translated from the French by G. M. Temmer

External Links:

MathReview (A. S. Wightman), ZentralBlatt

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§10.73(ii).

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Algorithm 346: F-test probabilities [S14]. Comm. ACM 12 (3), pp. 184–185.

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Notes:

Includes Algol program, maximum accuracy 12S. For a remark see ACM Trans. Math. Software 14(1988), pp. 288-289

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ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(iv).

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