Quantum Mechanics in Potential Representation and Applications

Contents
Preface
Introduction
Chapter 1: Quantum Nature of the Matter
	1.1 The Structure of Atoms
	1.2 The Schr¨odinger Equation
	1.3 The Fundamental Forces
	References
Chapter 2: Quantum Waves and Particles Diffusion in Physical Vacuum
	2.1 Introduction
	2.2 Diffusion of Quantum Waves
	2.3 The Quantum Diffusion of an Electron in the Hydrogen Atom
	2.4 Solution of the Quantum Diffusion Equation for the Tunnel Effect for a Rectangular Barrier
	2.5 Conclusions
	References
Chapter 3: Nuclear Forces
	3.1 The Interactions between Nucleons
	3.2 The Shell Model and Mean Field Potentials
	References
Chapter 4: Systems of Micro Particles
	References
Chapter 5: The Scattering Theory and Nuclear Reactions
	5.1 Introduction
	5.2 Nuclear Reactions and the Optical Model
	5.3 Inverse Tasks of Scattering
	References
Chapter 6: The Schrodinger Equation in Potential Representation
	6.1 Introduction
	6.2 Solution in the Case of s-Waves
	6.3 The Case of Large Nuclei
	6.4 Numerical Results and Conclusions
	References
Chapter 7: A General Solution of the Schrodinger Equation
	7.1 Introduction
	7.2 General Solution
	7.3 Numerical Results and Conclusions
	References
Chapter 8: The General Solutions for Positive and Negative Energies
	8.1 Introduction
	8.2 The Integral Equation for Positive Energies in the Potential Representation
	8.3 The Integral Equation for Negative Energies in the Potential Representation
	8.4 Numerical Results and Conclusions
	References
Chapter 9: The Connection between Scattering Matrices for Different Potentials
	9.1 Introduction
	9.2 Integral Equations for Positive Energies
	9.3 Connection of Potential Representation Method with Green’s Functions
	9.4 The Scattering Matrix
	References
Chapter 10: The Separation of the Scattering Matrix from the Coulomb Field
	10.1 Introduction
	10.2 Obtaining Integral Equations
	10.3 Obtaining the Scattering Matrix
	References
Chapter 11: The General Solution for Bound States of the Woods–Saxon Potential
	11.1 Introduction
	11.2 The Derivation of Integral Equations
	11.3 The Accuracy and Convergence of the Obtained Solutions
	11.4 Conclusions
	References
Chapter 12: The Perturbation Theory for Bound States
	12.1 Introduction
	12.2 Standard Green’s Functions
	References
Chapter 13: The Perturbation Method of Variation of Free Constants
	13.1 Green’s and Undefined Functions
	References
Chapter 14: Green’s Functions and Non-physical Solutions
	14.1 Introduction
	14.2 Non-physical Solutions of the Radial Schrodinger Equation
	14.3 Derivation of the Integral Equation
	14.4 Results and Conclusions
	References
Chapter 15: The Potential Representation Method for Non-spherical Perturbations
	15.1 Introduction
	15.2 Integral Equations for Negative Energies in the Potential Representation
	References
Chapter 16: Solutions with the Model Potential for the Potential Representation Method
	16.1 Introduction
	16.2 Modelling the Solutions of the Schrodinger Equation with the Harmonic Oscillator Potential
	16.3 Green’s Functions for the Potential Representation
	16.4 The Accuracy of the Solutions Obtained
	16.5 Conclusions
	References
Chapter 17: Potential Representation for the Coulomb Interactions
	17.1 Introduction
	17.2 Bounded Systems: The Two-Body Task
	17.3 The Many-Particles Task
	17.4 Solution for the Ground State of the Helium Atom
	17.5 Variation According to the Parameter Z
	References
Chapter 18: Transformations of the Hamiltonian for Jastrow’s Correlation Method
	18.1 Introduction
	18.2 Transformation of the Hamiltonian for He Atom
	18.3 Conclusions
	References
Chapter 19: Stability of Nuclei
	References
Chapter 20: Relativistic Corrections for Neutrons in the Harmonic Oscillator Well
	20.1 Introduction
	20.2 The Semi-relativistic Hamiltonian
	20.3 Results and Conclusions
	References
Chapter 21: Relativistic Corrections to One-Nucleon Energy Levels for 208Pb
	21.1 Introduction
	21.2 Semi-relativistic Equation
	21.3 Methods and Results
	21.4 Conclusions
	References
Chapter 22: Solutions for the Semi-relativistic Equations for the Heaviest Nuclei
	22.1 Introduction
	22.2 The Integral–Differential Semi-relativistic Equation
	22.3 Results and Conclusions
	References
Chapter 23: Stability of the Shells of the Heaviest Atomic Nuclei in the Semi-relativistic Model
	23.1 Introduction
	23.2 The Integral–Differential Semi-relativistic Equation
	23.3 Results and Conclusions
	References
Chapter 24: The Semi-relativistic Nuclear Shell Model for the Many-Particles Case
	24.1 Introduction
	24.2 The Solutions of Integral–Differential Semi-relativistic Equation for the Singular Potentials
	24.3 The System of Integral Semi-relativistic Equations in the Hartree–Fock Approach
	24.4 Conclusions
	References
Chapter 25: Relativistic Corrections for Different States of the Charmed and Bottom Mesons
	25.1 Introduction
	25.2 The Solutions of the Integral–Differential Semi-relativistic Equation
	25.3 The Approximate System of Integral Semi-relativistic Equations
	25.4 Semi-relativistic Model for Charmonium and Bottomonium
	25.5 Conclusions
	References
Bibliography of the Authors
Index