Position-momentum Heisenberg uncertainty in Gaussian enfoldments of Euclidian space

Journal of Mathematical Chemistry - Tập 51 - Trang 420-426 - 2012
Ramon Carbó-Dorca1
1Institut de Química Computacional, Univ. de Girona, Girona, Catalonia, Spain

Tóm tắt

Gaussian enfoldments have been derived from the form of general Gaussian functions centered at arbitrary positions in Euclidian space. Every point of Euclidian space acts in this way as the center of a Gaussian function defined in position space. Using the position-momentum Fourier transform in the quantum mechanical way and applied into the position functions of the Gaussian Euclidian enfoldment, the transform result provides a unique momentum Gaussian function, centered at the origin. In this way, the Euclidian enfoldment disappears in momentum space. Further analysis of the position-momentum relationship indicates that the product of the variances of the enfoldment in position and the corresponding momentum Fourier transform produces some kind of Heisenberg’s uncertainty relation.

Tài liệu tham khảo

Besalú E., Carbó-Dorca R.: J. Math. Chem. 49, 2231 (2011) Carbó-Dorca R., Besalú E.: J. Math. Chem. 49, 2244 (2011) Boys S.F.: Proc. R. Soc. (Lond.) A 200, 542 (1950) Shavitt I.: Method Comput. Phys. 2, 1 (1963) Carbó R., Leyda L., Arnau M.: Int. J. Quant. Chem. 17, 1185 (1980) P. Bultinck, X. Gironés, R. Carbó-Dorca, in Rev. Comput. Chem., vol. 21, eds. by K.B. Lipkowitz, R. Larter, T. Cundari (Wiley, Hoboken, USA, 2005), pp. 127–207 R. Carbó-Dorca, A. Gallegos, in Quantum Similarity and Quantum QSPR (QQSPR) Entry: 176, vol. 8, eds. by Meyers, R. Encyclopedia of complexity and systems science (Springer, New York, 2009), pp. 7422–7480 Carbó-Dorca R., Besalú E., Mercado L.D.: J. Comput. Chem. 32, 582 (2011) Constans P., Carbó R.: J. Chem. Inf. Comput. Sci. 35, 1046 (1995) P. Constans, X. Fradera, Ll. Amat, R. Carbó, in Quantum Molecular Similarity Measures (QMSM) and the Atomic Shell Approximation (ASA) in Proceedings of the 2nd. Girona Seminar on Molecular Similarity. July 1995. Advances in Molecular Similarity, vol. 1 (JAI PRESS INC., Greenwich (Conn.), 1996), p. 187. Amat Ll., Carbó-Dorca R.: J. Comput. Chem. 18, 2023 (1997) Amat Ll., Carbó-Dorca R.: J. Comput. Chem. 20, 911 (1999) Carbó-Dorca R., Besalú E.: J. Math. Chem. 50, 981 (2012) Carbó-Dorca R., Besalú E.: J. Math. Chem. 48, 914 (2010) Carbó-Dorca R., Besalú E.: J. Comput. Chem. 31, 2452 (2010) Carbó-Dorca R., Besalú E.: J. Math. Chem. 49, 836 (2011) Besalú E., Carbó-Dorca R.: J. Math. Chem. 49, 1769 (2011) R. Carbó-Dorca, E. Besalú, EMP as a similarity measure: a geometric point of view. IQC technical report TR-2012-9, J. Math. Chem. doi:10.1007/s10910-012-0089-4 Carbó-Dorca R.: J. Math. Chem. 36, 41 (2004) Carbó-Dorca R.: J. Math. Chem. 38, 89 (2005) Carbó-Dorca R.: J. Math. Chem. 39, 267 (2006) Carbó-Dorca R.: J. Math. Chem. 41, 209 (2007) I.M. Vinogradov (ed.), Encyclopaedia of Mathematics, vol. 4 (Kluwer, Dordrecht, 1989) A. Messiah, Mècanique Quantique (Tome I, Dunod, Paris, 1959), pp. 90, 400–401 Kaijsser P., Smith V.H. Jr.: Adv. Quantum. Chem. 10, 37 (1977) Thakkar A.: Adv. Chem. Phys. 128, 303 (2004)