MAPLE program for modelling hydrogen-like atoms in quantum mechanics with non-negative distribution function


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Abstract

The program is proposed for a realization of the symbolic algorithm based on the quantum mechanics with non-negative probability distribution function (QDF) and for calculations of energy levels for hydrogen-like atoms. The program is written up in the language MAPLE. In the framework of the algorithm an original Maple package for calculations of necessary functions, such as hydrogen wave functions, Sturmian functions and their Fourier-transforms, Clebsch-Gordan coefficients, etc. is proposed. Operators of observables are calculated on the basis of the QDF quantization rule. According to the Ritz method, eigenvalues of Ritz matrices represent spectral values of the quantity under investigation, i.e. energy. As an example, energy levels of hydrogen-like atoms are calculated and compared with experimental data retrieved from the NIST Atomic Spectra Database Levels Data. It turns out that this theory seems to be equivalent to the traditional quantum mechanics in regard to predictions of experimental values. However, the existence of a phase-space probabilistic quantum theory may be an important advance towards the explanation and interpretation of quantum mechanics.

About the authors

Alexander V Zorin

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: zorin@mx.rudn.ru

Associate Professor, Candidate of Sciences in Physics and Mathematics, Associate Professor of Peoples’ Friendship University of Russia (RUDN University)

6 Miklukho-Maklaya str., Moscow, 117198, Russian Federation

Nikolay P Tretyakov

The Russian Presidential Academy of National Economy and Public Administration; Russian State Social University

Email: trn11@rambler.ru

Associate Professor, Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Mathematics and Information Technologies of Russian State Social University

Prospect Vernadskogo, 82, Moscow 119571, Russian Federation; Wilhelm Pieck str., 4-1, Moscow, 119571, Russian Federation

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