Quantum Mechanics in Potential Representation and Applications
- Length: 272 pages
- Edition: 1
- Language: English
- Publisher: WSPC
- Publication Date: 2020-07-15
- ISBN-10: 9811216657
- ISBN-13: 9789811216657
- Sales Rank: #9808364 (See Top 100 Books)
This book is written with a focus on new mathematical methods and physical modeling that lay the groundwork for an interpretation to various experimental results and phenomena in nuclear physics, quantum mechanics, and particle physics. Summarized in three parts, the main topics of the book are as follows.
The first part importantly addresses scattering theory and nuclear reactions, with the usage of new potential representation method. This perturbation method offers the wave function as a product of the free particle solution and a function which depends on the interaction potential, allowing handy analytical expressions and integral equations for finding scattering matrices. It is highly applicable to the study of scattering and absorption of neutrons in atomic reactors, as well as the interactions between protons and nuclei by scattering processes in, for example, cyclotrons. The second part of the book concerns the perturbation method by variation of free constants and the semi-relativistic shell model of heavy nuclei in order to understand their stability. The last part is then furnished with the semi-relativistic model of mesons and relates to the binding energies of quarks in charm and bottom mesons.
This book would be a valuable resource for students and researchers on new mathematical methods in the theoretical unravelling of experiments concerning nuclei and mesons, nuclear reactors, radioactive isotopes, particle accelerators, new materials in electronics and healthcare products, as well as other practical applications of nuclear physics and quantum mechanics.
Cover page Title page Copyright Preface Introduction Contents Chapter 1: Quantum Nature of the Matter 1.1 The Structure of Atoms 1.2 The Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Index
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