Quantum Mechanics in Potential Representation and Applications

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.Contents: PrefaceIntroductionQuantum Nature of the MatterQuantum Waves and Particles Diffusion in Physical VacuumNuclear ForcesSystems of Micro ParticlesThe Scattering Theory and Nuclear ReactionsThe Schrödinger Equation in Potential RepresentationA General Solution of the Schrödinger EquationThe General Solutions for Positive and Negative EnergiesThe Connection between Scattering Matrices for Different PotentialsThe Separation of the Scattering Matrix from the Coulomb FieldThe General Solution for Bound States of the Woods-Saxon PotentialThe Perturbation Theory for Bound StatesThe Perturbation Method of Variation of Free ConstantsGreen's Functions and Non-physical SolutionsThe Potential Representation Method for Non-spherical PerturbationsSolutions with the Model Potential for the Potential Representation MethodPotential Representation for the Coulomb InteractionsTransformations of the Hamiltonian for Jastrow's Correlation MethodStability of NucleiRelativistic Corrections for Neutrons in the Harmonic Oscillator WellRelativistic Corrections to One-Nucleon Energy Levels of ²⁰⁸PbSolutions for the Semi-relativistic Equations for the Heaviest NucleiStability of the Shells of the Heaviest Atomic Nuclei in the Semi-relativistic ModelThe Semi-relativistic Nuclear Shell Model for Many-Particles CaseRelativistic Corrections for Different States of the Charmed and Bottom MesonsBibliography of the AuthorsIndex
Readership: Graduate students, researchers and professors working in the field of nuclear physics, quantum mechanics, and particle physics.Potential Scattering and Nuclear Reactions;Perturbation Theory in Potential Representation;Integral Equations;Semi-Relativistic Model of Nuclei and Mesons;Stability of Superheavy Nuclei00