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Non-perturbative Description of Quantum Systems

  • Book
  • © 2015

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Authors:
  1. Ilya Feranchuk

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

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  2. Alexey Ivanov

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

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  3. Van-Hoang Le

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

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  4. Alexander Ulyanenkov

    1. Karlsruhe, Germany

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  • Gives a detailed introduction and comprehensive description of non-perturbative operator method
  • Provides an extended review of other non-perturbative methods for description of quantum systems
  • Displays numerous applications of operator method for various problems of theoretical physics
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
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  2. Capabilities of Approximate Methods in Quantum Theory

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 1-25

  3. Basics of the Operator Method

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 27-80

  4. Applications of OM for One-Dimensional Systems

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 81-128

  5. Operator Method for Quantum Statistics

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 129-185

  6. Quantum Systems with Several Degrees of Freedom

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 187-214

  7. Two-Dimensional Exciton in Magnetic Field with Arbitrary Strength

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 215-249

  8. Atoms in the External Electromagnetic Fields

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 251-286

  9. Many-Electron Atoms

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 287-329

  10. Systems with Infinite Number of Degrees of Freedom

    • Ilya Feranchuk, Alexey Ivanov, Van-Hoang Le, Alexander Ulyanenkov
    Pages 331-358

  11. Back Matter

    Pages 359-362
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Keywords

About this book

This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

Authors and Affiliations

  • Physics Department, Belarusian State University, Minsk, Belarus

    Ilya Feranchuk

  • Physics Department, Belarusian National Technical University, Minsk, Belarus

    Alexey Ivanov

  • Department of Physics, Ho Chi Minh City University of Pedagogy, Ho Chi Minh City, Vietnam

    Van-Hoang Le

  • Karlsruhe, Germany

    Alexander Ulyanenkov

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