Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

Full text (ru)

M. V. Kuzmenko<sup>1

1</sup>Bogolyubov Institute for Theoretical Physics, National Academy of Science, Kyiv, Ukraine

Abstract: It is shown that the Schrödinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size has contradictions and is not strictly nonrelativistic, because it is based on the implicit assumption that the velocity of propagation of interactions is finite. In the framework of the model of the non-commutative operators of coordinates and momenta of different particles, the equation for wave function which has no above-mentioned drawbacks is deduced. The significant differences from solutions of the non-relativistic Schrödinger equation for large values of the interaction constant are found and the comparison of analogous results for hydrogenlike atoms with experimental data is carried out.

1. Landau L., Peierls R. Erweiterung des Unbestimmtheitsprinzips für die relativistische Quantentheorie. Zeitschrift für Physik 69 (1931) 56. https://doi.org/10.1007/BF01391513

2. Taylor J. R. An Introduction to Error Analysis (California: University Science Books Mill Valley, 1982).

3. Kuzmenko M. V. Nonrelativistic wave equation for a system of interacting particles. Phys. Rev. A 61 (2000) 014101. https://doi.org/10.1103/PhysRevA.61.014101

4. Messiah A. Quantum Mechanics. Vol. 1, 2 (Amsterdam: North-Holland Publisher Company, 1962).

5. Udem Th., Huber A., Gross B. et al. Phase-Coherent Measurement of the Hydrogen 1S-2S Transition Frequency with an Optical Frequency Interval Divider Chain. Phys. Rev. Lett. 79 (1997) 2646. https://doi.org/10.1103/PhysRevLett.79.2646

6. Eides M. I., Grotch H., Shelyuto V. A. Theory of Light Hydrogenlike Atoms. Phys. Rep. 342 (2001) 63. https://doi.org/10.1016/S0370-1573(00)00077-6

7. Stöhlker Th., Mokler P. H., Bosch F. et al. 1S Lamb Shift in Hydrogenlike Uranium Measured on Cooled, Decelerated Ion Beams. Phys. Rev. Lett. 85 (2000) 3109. https://doi.org/10.1103/PhysRevLett.85.3109

8. NIST Atomic Spectra Databases. http://physics.nist.gov