Abstract
In classical mechanics, the problems of the motion of objects with many degrees of freedom are formulated and solved using generalized coordinates rather than Cartesian coordinates. It is shown that a similar approach is also applicable to quantum mechanics. In both cases, the problem statement requires introduction of the potential function in appropriate coordinates and construction of the matrix of kinematic coefficients as a part of the classical expression of kinetic energy in the momentum representation. The possibility of the same problem statement is consistently discussed for the energy levels of polyatomic molecules. Some examples of its solution using generalized coordinates are provided.
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References
P. A. M. Dirac. Recollections of an Exciting Era. In: History of Twentieth Century Physics: Proceedings of the International [Summer] School of Physics “Enrico Fermi”. Cource LVII. New York: Academic Press, 1977, 109–146.
L. A. Gribov. Variability of basic statements of quantum theory of molecules [in Russian]. Moscow: Nobel Press, 2015.
L. A. Gribov. High Energy Chemistry, 2014, 48(4), 217.
L. A. Gribov. Doklady Physics, 2016, 61(3), 105.
L. A. Gribov. High Energy Chemistry, 2018, 52(1), 1.
E. Fermi. Notes on Quantum Mechanics. Chicago: University of Chicago Press, 1995.
G. R. Gruber. Found. Phys., 1971, 1(3), 227.
G. R. Gruber. Int. J. Theor. Phys., 1972, 6, 31.
G. R. Gruber. Int. J. Theor. Phys., 1973, 7, 253.
G. R. Gruber. Found. Phys., 1976, 6(3), 111.
F. J. Bloore and L. Routh. Nuovo cimento, 1975, 25B(1), 78.
K. R. Browinstein. Amer. J. Phys., 1976, 44, 677.
Yu. I. Ponomarev. Opt. Spectr., 1978, 45, 611.
V. D. Krivchenkov. Soviet Physics Uspekhi, 1981, 24(10), 860.
P. Villasenor-Consalez, J. Cisneros-Parra. Amer. J. Phys., 1981, 49, 754.
L. A. Gribov. J. Struct. Chem., 1992, 33(3), 164.
M. V. Volkenshtein, L. A. Gribov, M. A. Elyashevich, and B. I. Stepanov. Vibrations of Molecules [in Russian]. Moscow: Nauka, 1972.
L. A. Gribov. Vibrations of Molecules [in Russian]. Moscow: LIBROKOM, 2008.
M. A. Elyashevich and L. A. Gribov. Dokl. AN, 1966, 166(5), 1080.
L. A. Gribov. J. Struct. Chem., 2018, 59(3), 503.
B. K. Novosadov. Methods for solving the equations of quantum chemistry [in Russian]. Moscow: Nauka, 1988.
L. A. Gribov. J. Struct. Chem, 2018, 59(2), 272.
L. A. Gribov and I. V. Mikhailov. Butlerov Commun., 2018, 54(4), 29.
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Gribov, L.A. Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates. J Struct Chem 60, 356–364 (2019). https://doi.org/10.1134/S0022476619030028
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DOI: https://doi.org/10.1134/S0022476619030028