On some non-Gaussian wave packets

• Autorzy: Patkowski A. E.

Identyfikatory

DOI

10.1515/jaa-2018-0011

• Języki publikacji: EN

Abstrakty

EN

We expand on a previous study by offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function associated with a recent work by the present author and M. Wolf.

Słowa kluczowe

EN

Fourier integrals; Schrödinger equation; free particle wave packet

PL

całki Fouriera; równanie Schrodingera

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 1
• Strony: 109--114
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Patkowski A. E.

• 1390 Bumps River Road, Centerville, MA 02632, USA,

Bibliografia

• [1] G. Andrews, R. Askey and R. Roy, Special Functions , Encyclopedia Math. Appl. 71, Cambridge University Press, 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, Q. J. Pure Appl. Math. (1871), 238-343.
• [4] M. L. Glasser, Time evolution of a non-gaussian wave packet, Phys. Lett. A 76A (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] A. Patkowski, On Integrals Associated with the free particle wave packet, preprint (2016), https://arxiv.org/abs/1606.03789.
• [8] A. Patkowski and M. Wolf, Some Remarks on Glaisher-Ramanujan Type Integrals, Comput. Methods Sci. Technol. 22 (2016), no. 2, 103-108.
• [9] S. Ramanujan, Some definite integrals connected with Gauss’s sums, Messenger Math. 44 (1915), 75-85.
• [10] R. W. Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples , 2nd ed., Oxford University Press, Oxford, 2006.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).