On integrals associated with the free particle wave packet

• Autorzy: Patkowski Alexander E.

Identyfikatory

DOI

10.1515/jaa-2020-2014

• Języki publikacji: EN

Abstrakty

EN

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.

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: 2020
• Tom: Vol. 26, nr 2
• Strony: 257--262
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Patkowski Alexander E.

• 1390 Bumps River Rd., Centerville, MA 02632, USA,

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).