On Spatial Transformations of Atoms
- PDF / 1,521,696 Bytes
- 6 Pages / 595.276 x 790.866 pts Page_size
- 64 Downloads / 215 Views
ON SPATIAL TRANSFORMATIONS OF ATOMS V. V. Skobelev, V. P. Krasin, and S. V. Kopylov
UDC 539.12
Based on the experimentally established existence of atoms with spatially one- and two-dimensional electronic structures that can be paired with conventional three-dimensional atoms, a formal theoretical substantiation is proposed in favor of the possibility of simultaneous presence of all three types of atoms with spatial dimension DI D1, D 2, D3 . Despite the fundamental difference in the computational procedure, the results of the present study seem to be quite adequate being a significant addition to the results of previous V. V. Skobelev’s works. The conclusions of the work can be verified in experiments, though the principal feasibility of such experiments is not obvious. This last problem needs further substantiation and is not discussed in this work. Keywords: atoms, dimensionality of space, probability, transitions.
INTRODUCTION Recently intensive theoretical investigations have been carried out in the literature concerning the existence and properties of atoms with spatially one- and two-dimensional electronic structures, that is, atoms in spaces with dimension DI D1, D 2 (see V. V. Skobelev’s works [1–4] and the literature cited therein). This is primarily explained by successful experiments on creation of such atoms in [5–8], which in a suitable experimental situation (for example, with the help of extended or flat traps) are formed in vapors simultaneously with conventional threedimensional atoms. In this connection, a natural question arises on the possibility of simultaneous existence of all three spatial configurations of atoms. In [9]1 this problem has already been discussed; however, considerations were partly incomplete (see Section 2). In the present work, we attempt to fill this gap in the theory being developed.
1. GENERAL PROBABILITY RELATIONSHIPS For completeness of presentation, in this Section we partly repeat some discourse presented in [9] with some modifications. According to the main principles of quantum mechanics [10], the simultaneous existence of the three ( D1, D 2, and D3 ) spatial configurations (dimensions) of a system of identical atoms, as in the case of two configurations, assumes the presence of a certain probability of transition W of an atom from one spatial configuration to another. Designating the probability of transition of an atom from the state with spatial dimension DI to the state
1
Intermediate formula (28) from [9] was inaccurate: in the parentheses in the right side of the formula instead
of “ 2xF 2 ” should be “ 2xfF ”; however, basic equation (31) and Eq. (34а) following from it were written accurately.
Moscow Polytechnic University, Moscow, Russia, e-mail: [email protected]; [email protected]; [email protected]. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 10–13, July, 2020. Original article submitted April 13, 2019. 1112
1064-8887/20/6307-1112 2020 Springer Science+Business Media, LLC
with dimension DJ by W (i j ) ,
Data Loading...
