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International Conference on Physics and Mechanics of New Materials and Their Applications

PHENMA 2017: Advanced Materials pp 145–159Cite as

Density Matrix Method in Atom Theory

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Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 207))

Abstract

In this work, we apply a new variational principle that allows us to find the distribution function of electron in an arbitrary atom. This principle is based on the method of density matrix . Using the density matrix , we found the energy of the electrons in an atom, entropy and thermodynamic potential. The main idea of this article is that all two-electron matrices must be anti-symmetric. This refers to the two-electron Hamiltonian. This applies to Slater two-particle wave function. We found the equation for the distribution function of electrons at the quantum orbits. This equation can be obtained in two cases. In the first case, based on the density matrix of the first order, this equation is obtained only for the distribution function. In the second case two equations are obtained, which include distribution function and correlation function. The distribution function of electrons in the atom is similar to the function of Fermi–Dirac for electrons in a solid. In this work we apply a new approach to calculate the energy levels of electron in an arbitrary atom. This approach is also based on the method of density matrix .

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Author information

Authors and Affiliations

  1. Moscow Aviation Institute, Volokolamskoye Shosse, 4, Moscow, 125871, Russia

    Boris V. Bondarev

Authors
  1. Boris V. Bondarev
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Correspondence to Boris V. Bondarev .

Editor information

Editors and Affiliations

  1. I. I. Vorovich Mathematics, Mechanics and Computer Sciences Institute, Southern Federal University, Rostov-on-Don, Russia

    Ivan A. Parinov

  2. Department of Microelectronics Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan

    Shun-Hsyung Chang

  3. Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, Jabalpur, Madhya Pradesh, India

    Vijay K. Gupta

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Bondarev, B.V. (2018). Density Matrix Method in Atom Theory. In: Parinov, I., Chang, SH., Gupta, V. (eds) Advanced Materials . PHENMA 2017. Springer Proceedings in Physics, vol 207. Springer, Cham. https://doi.org/10.1007/978-3-319-78919-4_12

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