Introduction to quantum mechanics : in chemistry, materials science, and biology

Introduction to Quantum Mechanics, 2nd Edition provides an accessible, fully updated introduction to the principles of quantum mechanics. It outlines the fundamental concepts of quantum theory, discusses how these arose from classic experiments in chemistry and physics, and presents the quantum-mechanical foundations of current scientific developments. Beginning with a solid introduction to the key principles underpinning quantum mechanics in Part 1, the book goes on to expand upon these in Part 2, where fundamental concepts such as molecular structure and chemical bonding are discussed. Finally, Part 3 discusses applications of this quantum theory across some newly developing applications, including chapters on Density Functional Theory, Statistical Thermodynamics and Quantum Computing. Drawing on the extensive experience of its expert author, Introduction to Quantum Mechanics, 2nd Edition is a lucid introduction to the principles of quantum mechanics for anyone new to the field, and a useful refresher on fundamental knowledge and latest developments for those varying degrees of background. Presents a fully updated accounting that reflects the most recent developments in Quantum Theory and its applications Includes new chapters on Special Functions, Density Functional Theory, Statistical Thermodynamics and Quantum Computers Presents additional problems and exercises to further support learning Contents Preface to the 1st edition Preface to the 2nd edition About the author 1 Atoms and photons: origins of the quantum theory 1.1 Atomic and subatomic particles 1.2 Electromagnetic waves 1.3 Three failures of classical physics 1.4 Blackbody radiation 1.5 The photoelectric effect 1.6 Line spectra Supplement 1A. Maxwell's equations Supplement 1B. The Planck radiation law 2 Waves and particles 2.1 The double-slit experiment 2.2 Wave-particle duality 2.3 The Schrödinger equation 2.4 Operators and eigenvalues 2.5 The wavefunction Chapter 2. Exercises 3 Quantum mechanics of some simple system 3.1 The free particle 3.2 Particle in a box 3.3 Free-electron model 3.4 Particle in a three-dimensional box Supplement 3A. Finite square-well potential Chapter 3. Exercises 4 Principles of quantum mechanics 4.1 Hermitian operators 4.2 Eigenvalues and eigenfunctions 4.3 Expectation values 4.4 More on operators 4.5 Postulates of quantum mechanics 4.6 Dirac bra-ket notation 4.7 The variational principle 4.8 Spectroscopic transitions Supplement 4A. Perturbation theory Supplement 4B. Time-dependent perturbation theory for radiative transitions Chapter 4. Exercises 5 Special functions 5.1 Gaussian functions 5.2 The gamma function 5.3 The Dirac deltafunction 5.4 Leibniz's formula 5.5 Hermite polynomials 5.6 Spherical polar coordinates 5.7 Legendre polynomials 5.8 Spherical harmonics 5.9 Laguerre polynomials 5.10 Series solutions of differential equations 5.11 Bessel functions 5.12 Spherical Bessel functions Supplement 5A. Particle in a disk Supplement 5B. Particle in an infinite spherical well Supplement 5C. Particle in a deltafunction well 6 The harmonic oscillator 6.1 Classical oscillator 6.2 Quantum harmonic oscillator 6.3 Harmonic-oscillator eigenfunctions and eigenvalues 6.4 Operator formulation of harmonic oscillator 6.5 Quantum theory of radiation Supplement 6A. Anharmonic oscillator Chapter 6. Exercises 7 Angular momentum 7.1 Particle in a ring 7.2 Free electron model for aromatic molecules 7.3 Rotation in three dimensions 7.4 Theory of angular momentum 7.5 Operator derivation of angular momentum eigenvalues 7.6 Electron spin 7.7 Pauli spin algebra 7.8 Addition of angular momenta 8 The hydrogen atom and atomic orbitals 8.1 Atomic spectra 8.2 The Bohr atom 8.3 Quantum mechanics of hydrogenlike atoms 8.4 Hydrogen-atom ground state 8.5 Schrödinger equation for atomic orbitals 8.6 p- and d-orbitals 8.7 Summary on atomic orbitals 8.8 Reduced mass Chapter 8. Exercises 9 The helium atom 9.1 Experimental energies 9.2 Schrödinger equation and variational calculations 9.3 Spinorbitals and the exclusion principle 9.4 Excited states of helium Chapter 9. Exercises 10 Atomic structure and the periodic law 10.1 Slater determinants 10.2 Self-consistent field theory 10.3 Aufbau principles 10.4 Atomic configurations and term symbols 10.5 Periodicity of atomic properties 10.6 Relativistic effects 10.7 Spiral form of the periodic table Chapter 10. Exercises 11 The chemical bond 11.1 The hydrogen molecule 11.2 Valence bond theory 11.3 Hybrid orbitals and molecular geometry 11.4 Hypervalent compounds 11.5 Boron hydrides 11.6 Valence-shell model 11.7 Transition metal complexes 11.8 The hydrogen bond 11.9 Critique of valence-bond theory Chapter 11. Exercises 12 Molecular orbital theory of diatomic molecules 12.1 The hydrogen molecule-ion 12.2 The LCAO approximation 12.3 MO theory of homonuclear diatomic molecules 12.4 Variational computation of molecular orbitals 12.5 Heteronuclear molecules 12.6 Electronegativity Chapter 12. Exercises 13 Polyatomic molecules and solids 13.1 Hückel molecular orbital theory 13.2 Conservation of orbital symmetry; Woodward-Hoffmann rules 13.3 Band theory of metals and semiconductors 13.4 Computational chemistry Chapter 13. Exercises 14 Density functional theory 14.1 Thomas-Fermi model 14.2 The Hohenberg-Kohn theorems 14.3 Density functional theory 14.4 Slater's X-alpha method 14.5 The Kohn-Sham equations 14.6 Chemical potential Chapter 14. Exercises 15 Molecular symmetry 15.1 The ammonia molecule 15.2 Mathematical theory of groups 15.3 Group theory in quantum mechanics 15.4 Molecular orbitals for ammonia 15.5 Selection rules 15.6 The water molecule 15.7 Walsh diagrams 15.8 Molecular symmetry groups Low-symmetry groups Rotational groups Dihedral groups Groups of higher symmetry 15.9 Dipole moments and optical activity 15.10 Character tables Chapter 15. Exercises 16 Molecular spectroscopy 16.1 Vibration of diatomic molecules 16.2 Vibration of polyatomic molecules 16.3 Rotation of diatomic molecules 16.4 Rotation-vibration spectra 16.5 Molecular parameters from spectroscopy 16.6 Rotation of polyatomic molecules 16.7 Electronic excitations 16.8 Lasers 16.9 Raman spectroscopy Chapter 16. Exercises 17 Statistical thermodynamics 17.1 Quantum mechanics 17.2 Thermodynamic functions 17.3 The Boltzmann distribution 17.4 Molar partition function 17.5 Ideal monatomic gas 17.6 The Sakur-Tetrode equation 17.7 The Born-Oppenheimer approximation 17.8 Rotation of diatomic molecules 17.9 Rotation of polyatomic molecules 17.10 Molecular vibration 17.11 Electronic contributions 17.12 Summary Supplement 17A. Low-temperature heat capacity of hydrogen molecules Chapter 17. Exercises 18 Nuclear magnetic resonance 18.1 Magnetic properties of nuclei 18.2 Nuclear magnetic resonance 18.3 The chemical shift 18.4 Spin-spin coupling 18.5 Mechanism for spin-spin interactions 18.6 Magnetization and relaxation processes 18.7 Pulse techniques and Fourier transforms 18.8 Two-dimensional NMR 18.9 Magnetic resonance imaging Chapter 18. Exercises 19 Wonders of the quantum world 19.1 The Copenhagen interpretation 19.2 Superposition 19.3 Schrödinger's Cat 19.4 Einstein-Podolsky-Rosen experiment 19.5 Bell's theorem 19.6 Aspect's experiment 19.7 Multiple photon entanglement 19.8 Philosophical problems of quantum theory Chapter 19. Exercises 20 Quantum computers 20.1 Qubits 20.2 Quantum gates and circuits 20.3 Simulation of a Stern-Gerlach experiment 20.4 Quantum Fourier transform 20.5 Phase estimation algorithm 20.6 Many-electron systems 20.7 Atomic and molecular Hamiltonians 20.8 Time-evolution of a quantum system 20.9 Trotter expansions 20.10 Simulations of molecular structure Answers to exercises Chapter 2 Chapter 3 Chapter 4 Chapter 6 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Suggested references Index Introduction to Quantum Mechanics, Second Edition presents an accessible, fully-updated introduction on the principles of quantum mechanics. The book outlines the fundamental concepts of quantum theory, discusses how these arose from classic experiments in chemistry and physics, and presents the quantum-mechanical foundations of many key scientific techniques. Chapters cover an introduction to the key principles underpinning quantum mechanics, differing types of molecular structures, bonds and behaviors, and applications of quantum mechanical theory across a number of important fields, including new chapters on Density Functional Theory, Statistical Thermodynamics and Quantum Computing.Drawing on the extensive experience of its expert author, this book is a reliable introduction to the principles of quantum mechanics for anyone new to the field, and a useful refresher on fundamental knowledge and latest developments for anyone more experienced in the field. - Presents a fully updated accounting that reflects the most recent developments in Quantum Theory and its applications- Includes new chapters on Special Functions, Density Functional Theory, Statistical Thermodynamics and Quantum Computers- Presents additional problems and exercises to further support learning Introduction To Quantum Mechanics, Second Edition Presents An Accessible, Fully-updated Introduction On The Principles Of Quantum Mechanics. The Book Outlines The Fundamental Concepts Of Quantum Theory, Discusses How These Arose From Classic Experiments In Chemistry And Physics, And Presents The Quantum-mechanical Foundations Of Many Key Scientific Techniques. Chapters Cover An Introduction To The Key Principles Underpinning Quantum Mechanics, Differing Types Of Molecular Structures, Bonds And Behaviors, And Applications Of Quantum Mechanical Theory Across A Number Of Important Fields, Including New Chapters On Density Functional Theory, Statistical Thermodynamics And Quantum Computing. Drawing On The Extensive Experience Of Its Expert Author, This Book Is A Reliable Introduction To The Principles Of Quantum Mechanics For Anyone New To The Field, And A Useful Refresher On Fundamental Knowledge And Latest Developments For Anyone More Experienced In The Field. Presents A Fully Updated Accounting That Reflects The Most Recent Developments In Quantum Theory And Its Applications Includes New Chapters On Special Functions, Density Functional Theory, Statistical Thermodynamics And Quantum Computers Presents Additional Problems And Exercises To Further Support Learning "This book provides an up-to-date introduction to the principles of quantum mechanics for undergraduates and first-year graduate students in chemistry, materials science, biology, and related fields. The presentation of quantum mechanics in broadly based to make it pertinent as well to students in materials science, biology and related fields."--Jacket