This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.
Contents: - Preface
- Introduction
- Nonrelativistic Quantum Mechanics
- Scattering of Light and Particles
- Atom in Magnetic Field
- Relativistic Quantum Mechanics
- Quantum Postulates and Attractors
- Attractors of Hamiltonian PDEs
- Appendices:
- Old Quantum Theory
- The Noether Theory of Invariants
- Perturbation Theory
- Bibliography
- Index
Readership: Discipline/profession: Physics and Mathematics. Sector: university, academia and industry. Level: Graduate students and advanced undergraduate students physicists, chemists and mathematicians, lecturers in Quantum Mechanics.Schrödinger Equation;Maxwell Equations;Pauli Equation;Dirac Equation;Maxwell-Schrödinger Equations;Semiclassical Asymptotics;Hamilton-Jacobi Equation;Charge;Electron;Nucleous; Barion;Momentum;Angular Momentum;Spin;Quantum Transitions;Wave-Particle Duality; Wave Function;Hydrogen Spectrum;Probabilistic Interpretation;Magnetic Moment;Normal Zeeman Effect; Anomalous Zeeman Effect;Diffraction of Electrons;Kirchhoff Approximation;Aharonov-Bohm Shift; Hamiltonian Equation; Hamiltonian Functional;Hamiltonian Structure;Hamiltonian Canonical Form;Hamiltonian Partial Differential Equations;Symmetry Group;Distribution;Fourier Transform;Variational Derivatives;Diffraction;Green Function; Sommerfeld Radiation Condition;Limiting Amplitude Principle;Limiting Absorption Principle;Attractor;Stationary State;Stationary Orbit;Soliton;Adiabatic Effective Dynamics;Mass-Energy Equivalence; Rotation Group;Lorentz Group;Lie Group;Lie Algebra; Representation of Lie Group;Representation of Lie Algebra;Rotational Covariance;Lorentz Covariance;Pauli Theorem;Clebsch-Gordan Theorem;Wiener Tauberian Theorem;Titchmarsh Convolution Theorem0
Key Features:- Deep and meaningful motivation of all introduced concepts and constructions, and application to basic quantum phenomena with simplest straightforward calculations and full explanations of all mathematical methods used
- A clear demonstration of the balance between empirical facts and adequate mathematical tools
- A unified style of presentation relying on the Hamiltonian formalism which lies in the ground of modern Quantum Theory
- Systematic application and explanation of limiting amplitude and limiting absorption principles which are cardinal tools of modern diffraction and scattering theory
- Discussion of dynamical interpretation of basic Quantum Postulates in the context of selfconsistent coupled Maxwell-Schrödinger equations
- Numerous problems and exercises clarify and complete the main exposition, and makes the book suitable for individual study
