Calculation of transition probabilities in quantum mechanics with a nonnegative distribution function in the Maple computer algebra system
A. V. Zorinabc, N. P. Tret'yakovacb
a Peoples' Friendship University of Russia, Moscow
b Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Moscow
c Russian State Social University, Moscow
In the Maple computer algebra system, an algorithm is implemented for symbolic and numerical computations for finding the transition probabilities for hydrogen-like atoms in quantum mechanics with a nonnegative quantum distribution function (QDF). Quantum mechanics with a nonnegative QDF is equivalent to the standard theory of quantum measurements. However, the presence in it of a probabilistic quantum theory in the phase space gives additional possibilities for calculating and interpreting the results of quantum measurements. The methods of computer algebra seem to be necessary for the relevant calculations. The calculation of the matrix elements of operators is necessary for determining the energy levels, oscillator strengths, and radiation transition parameters for atoms and ions with an open shell. Transition probabilities are calculated and compared with experimental data. They are calculated using the Galerkin method with the Sturm functions of the hydrogen atom as coordinate functions. The verification of the model showed good agreement between the calculated and experimentally measured transition probabilities.
computer algebra, Maple, quantum mechanics, energy levels, quantization, transition probabilities, hydrogen-like atoms.
Computational Mathematics and Mathematical Physics, 2020, 60:1, 82–89
A. V. Zorin, N. P. Tret'yakov, “Calculation of transition probabilities in quantum mechanics with a nonnegative distribution function in the Maple computer algebra system”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 88–95; Comput. Math. Math. Phys., 60:1 (2020), 82–89
Citation in format AMSBIB
\by A.~V.~Zorin, N.~P.~Tret'yakov
\paper Calculation of transition probabilities in quantum mechanics with a nonnegative distribution function in the Maple computer algebra system
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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