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Non-perturbative Description of Quantum Systems pp 27–80Cite as

Basics of the Operator Method

Part of the Lecture Notes in Physics book series (LNP,volume 894)

Abstract

The majority of approximate methods for the solution of Schrödinger equation (SE) demonstrated in Chap. 1 is not sufficiently universal and theirs applications in the case of system with many degrees of freedom are bound up with serious difficulties. In the following chapters we consider the method which is proposed as an universal procedure for transformation of the perturbation series and its further applications for various quantum systems. We call this technique operator method (OM) in the sense that all calculations are reduced to the algebraic manipulations with the operator matrix elements without solving any differential or integral equations, in zeroth-order approximation as well as in calculating the successive approximations. The results prove that the OM zeroth-order approximation provides an uniformly fitted estimation of the SE eigenvalues and eigenfunctions in the entire range of the Hamiltonian parameters.

Keywords

  • Wave Function
  • Matrix Element
  • State Vector
  • Operator Method
  • Canonical Transformation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 2.1
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Authors and Affiliations

  1. Physics Department, Belarusian State University, Minsk, Belarus

    Ilya Feranchuk

  2. Physics Department, Belarusian National Technical University, Minsk, Belarus

    Alexey Ivanov

  3. Department of Physics, Ho Chi Minh City University of Pedagogy, Ho Chi Minh City, Vietnam

    Van-Hoang Le

  4. Atomicus GmbH, Karlsruhe, Germany

    Alexander Ulyanenkov

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  1. Ilya Feranchuk
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  3. Van-Hoang Le
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  4. Alexander Ulyanenkov
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Feranchuk, I., Ivanov, A., Le, VH., Ulyanenkov, A. (2015). Basics of the Operator Method. In: Non-perturbative Description of Quantum Systems. Lecture Notes in Physics, vol 894. Springer, Cham. https://doi.org/10.1007/978-3-319-13006-4_2

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