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Oscillator Representation in Quantum Physics

  • Book
  • © 1995

Overview

Authors:
  1. M. Dineykhan

    1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia

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  2. G. V. Efimov

    1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia

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  3. G. Ganbold

    1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia

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  4. S. N. Nedelko

    1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia

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Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 26)

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    1. Introduction

      Pages 1-6

  4. Back Matter

    Pages 121-123
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  5. The Gaussian Equivalent Representation of Functional Integrals in Quantum Physics

    1. Front Matter

      Pages 125-125
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    2. Path Integrals in Quantum Physics

      Pages 127-144

    3. The Gaussian Equivalent Representation of Functional Integrals

      Pages 145-155

    4. The Polaron Problem

      Pages 157-178

    5. The Character of the Phase Transition in Two- and Three-Dimensional Ï•4 Theory

      Pages 179-188

    6. Wave Propagation in Randomly Distributed Media

      Pages 189-196

    7. Bound States in QFT

      Pages 197-202

  6. Back Matter

    Pages 203-206
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  7. Oscillator Representation in Quantum Mechanics

    1. Front Matter

      Pages 207-207
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    2. The Oscillator in Quantum Mechanics

      Pages 209-213
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Keywords

About this book

The investigation ofmost problems of quantum physics leads to the solution of the Schrodinger equation with an appropriate interaction Hamiltonian or potential. However, the exact solutions are known for rather a restricted set of potentials, so that the standard eternal problem that faces us is to find the best effective approximation to the exact solution of the Schrodinger equation under consideration. In the most general form, this problem can be formulated as follows. Let a total Hamiltonian H describing a relativistic (quantum field theory) or a nonrelativistic (quantum mechanics) system be given. Our problem is to solve the Schrodinger equation Hlft = Enlftn, n i. e. , to find the energy spectrum {En} and the proper wave functions {lft } n including the'ground state or vacuum lft = 10). The main idea of any ap­ o proximation technique is to find a decomposition in such a way that Ha describes our physical system in the "closest to H" manner, and the Schrodinger equation HolJt. (O) = E(O)lJt. (O) n n n can be solved exactly. The interaction Hamiltonian HI is supposed to give small corrections to the zero approximation which can be calculated. In this book, we shall consider the problem of a strong coupling regime in quantum field theory, calculations ofpath or functional integrals over the Gaussian measure and spectral problems in quantum mechanics. Let us con­ sider these problems briefly.

Authors and Affiliations

  • Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research (JINR), Dubna, Russia

    M. Dineykhan, G. V. Efimov, G. Ganbold, S. N. Nedelko

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