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Abstrakty
We discuss some properties of integrals associated with the free particle wave packet, ψ(x, t), which are solutions to the time-dependent Schrödinger equation for a free particle. Some noteworthy discussion is made in relation to integrals which have appeared in the literature. We also obtain formulas for half-integer arguments of the Riemann zeta function.
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Rocznik
Tom
Strony
257--262
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
Bibliografia
- [1] G. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia Math. Appl. 71, Cambridge University, New York, 1999.
- [2] G. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook. Part IV, Springer, New York, 2013.
- [3] J. W. L. Glaisher, On the summation by definite integrals of geometric series of the second and higher order, Quart. J. Pure Appl. Math. (1871), 238-343.
- [4] M. L. Glasser, Time evolution of a non-Gaussian wave packet, Phys. Lett. A. 76 (1980), no. 3-4, 219-220.
- [5] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed., Academic Press, New York, 2007.
- [6] F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974.
- [7] S. Ramanujan, Some definite integrals connected with Gauss’s sums, Mess. Math. 44 (1915), 75-85.
- [8] R. W. Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples, 2nd ed., Oxford University, Oxford, 2006.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-88713cb6-76a8-4e91-934a-7892fdd88ab9