Analytical and numerical methods are used to analyze for the first time the possibility of the existence of a one-dimensional hydrogen molecule H2. The conclusions of this work can in principle be verified experimentally: for example, one-dimensional Na atoms were experimentally obtained quite recently. Because of fundamental computational difficulties associated with the divergence of one-dimensional integrals at small distances, only the very possibility of the existence of such molecules is proven without specification of their energy characteristics (binding energy, etc.).
Similar content being viewed by others
References
A. Görlitz, J. M. Vogels, A. E. Leanhardt, et al. // Phys. Rev. Lett., 87, 130402 (2001).
U. Eichmann, V. Lange, and W. Sandner, Phys. Rev. Lett., 64, 274 (1990).
V. V. Skobelev, J. Exp. Тheor. Phys., 124, No. 6, 877 (2017).
V. V. Skobelev, J. Exp. Тheor. Phys., 126, No. 3, 333 (2018).
V. V. Skobelev, Russ. Phys. J., 61, No. 5, 887 (2018).
A. A. Sokolov, Yu. M. Loskutov, and I. M. Ternov, Quantum Mechanics Holt, Rinehart & Winston, Austin (1966).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, London (1977).
E. A. Hylleraas, Z. Phys., 63, 291 (1930).
E. A. Hylleraas, Z. Phys., 63, 771 (1930).
V. V. Skobelev, J. Exp. Тheor. Phys., 126, No. 5, 645 (2018).
V. V. Skobelev, Russ. Phys. J., 60, No. 9, 1495 (2017).
R. London, Am. J. Phys., 27, 649 (1959).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Cambridge, MA (2000).
V. V. Skobelev, Russ. Phys. J., 61, No. 2, 312 (2018).
V. V. Skobelev, Russ. Phys. J., 58, No. 2, 163 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 73–80, September, 2019.
Rights and permissions
About this article
Cite this article
Skobelev, V.V. On the Question of the Existence of a One-dimensional Hydrogen Molecule. Russ Phys J 62, 1613–1622 (2020). https://doi.org/10.1007/s11182-020-01883-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-020-01883-1