This book presents quantum mechanics through a systematic progression from classical atomic models to modern quantum theory. Beginning with foundational concepts, the text develops Schrödinger's equation and its applications to fundamental quantum systems. Mathematical rigor is balanced with physical interpretation throughout. * Detailed derivations of quantum mechanical principles * Comprehensive treatment of particle systems, rigid rotators, and harmonic oscillators * In-depth analysis of hydrogen atom wavefunctions and multi-electron systems * Applications to rotational, vibrational, and…mehr
This book presents quantum mechanics through a systematic progression from classical atomic models to modern quantum theory. Beginning with foundational concepts, the text develops Schrödinger's equation and its applications to fundamental quantum systems. Mathematical rigor is balanced with physical interpretation throughout. * Detailed derivations of quantum mechanical principles * Comprehensive treatment of particle systems, rigid rotators, and harmonic oscillators * In-depth analysis of hydrogen atom wavefunctions and multi-electron systems * Applications to rotational, vibrational, and electronic spectroscopy * Comparative presentation of Valence Bond and Molecular Orbital theories Ideal for advanced undergraduate and graduate students in chemistry and physics. This title has been co-published with Manakin Press. Taylor & Francis does not sell or distribute the print edition in India, Pakistan, Nepal, Bhutan, Sri Lanka and Bangladesh.
Dr. Amita Dua is Associate Professor in the Department of Chemistry at Dyal Singh College, University of Delhi. She holds M.Sc. and Ph.D. in Chemistry and specializes in quantum mechanics and molecular spectroscopy.
Inhaltsangabe
Chapter 1 Classical Mechanics 1.1 Dalton's Atomic Theory 1.2 What are Classical Mechanics and Quantum Mechanics? 1.3 J.J. Thomson Model of Atom 1.4 Rutherford's Nuclear Model of Atom - Discovery of Nucleus 1.5 Developments Leading to The Bohr Model of Atom 1.6 Bohr Model of Atom 1.7 Sommerfeld Theory or Bohr-Sommerfeld Theory Chapter 2 Towards Quantum Mechanics 2.1 Reasons for The Failure of Classical Model of Atom or Bohr Model of Atom 2.2 Developments Leading to Quantum Mechanical Model of Atom 2.3 De-Broglie's Dual Nature of Matter 2.4 Heisenberg's Uncertainty Principle Chapter 3 Introduction to Quantum Mechanics 3.1 Necessity of Quantum Mechanics 3.2 Schrodinger Wave Equation 3.3 Derivation of Time Independent Schrodinger Wave Equation 3.4 Physical Significance of Wavefunction ( ) and Probability Density ( ²) 3.5 Concept of Atomic Orbital 3.6 Quantum Mechanical Model of Atom 3.7 Eigen Value and Eigen Wavefunction 3.8 Normalised, Orthogonal and Orthonormal Wavefunction 3.9 Operators 3.10 Postulates of Quantum Mechanics 3.11 Derivation of Time Independent Schrodinger Wave Equation on The Basis of Postulates of Quantum Mechanics 3.12 Steady State Schrödinger Wave Equation Chapter 4 Particle in a Box: Quantisation of Translational Energy 4.1 Application of Postulates of Quantum Mechanics to Simple System 4.2 Operation of Quantum Mechanics 4.3 Introduction to Translational Motion of a Particle 4.4 Particle in One Dimensional Box: Quantisation of Translational Energy 4.5 Particle in Two-dimensional 4.6 Particle in Three Dimensional Box 4.7 Free Particle Chapter 5 Rigid Rotator and Rotational Spectra 5.1 Introduction 5.2 Classical Treatment of Rigid Rotator 5.3 Quantum Mechanical Treatment: Schrödinger Wave Equation for Rigid Rotator 5.4 Wavefunction of Rigid Rotator 5.5 Rotational Energy of the Rigid Rotator 5.6 Rotational Energy Levels 5.7 Rotational Selection Rules 5.8 Rotational Spectra of Rigid Diatomic Molecule 5.9 Microwave Active Molecules or Types of Molecules Showing Rotational Spectra 5.10 Parameters Calculated from Rotational Spectra 5.11 Isotopic Effect 5.12 Application of Microwave Radiation: Microwave Oven Chapter 6 Linear Harmonic Oscillator and Vibrational Spectra 6.1 Introduction 6.2 Classical Treatment of Linear Harmonic Oscillator 6.3 Quantum Mechanical Treatment: Schrödinger Wave Equation for Linear Harmonic Oscillator 6.4 Solution of Schrödinger Wave Equation: Vibrational Energy and Wavefunction of The Linear Harmonic Oscillator 6.5 Wavefunction Plots for Linear Harmonic Oscillator 6.6 Probability Plots for Linear Harmonic Oscillator 6.7 Symmetry of The Vibrational Wavefunction 6.8 Calculation of Properties of Linear Harmonic Oscillator 6.9 Orthonormal Sets of Wavefunction 6.10 Virial Theorem 6.11 Vibrational Energy and Zero Point Energy for Linear Harmonic Oscillator 6.12 Vibrational Selection Rule 6.13 Vibrational Spectra of Linear Harmonic Oscillator 6.14 Infrared Active Molecules or Types of Molecules Showing Vibrational Spectra Chapter 7 "Hydrogen Atom": Quantisation of Electronic Energy 7.1 Necessity of Replacing Bohr Theory 7.2 Setting of Schrodinger Equation for Hydrogen Atom 7.3 Quantum Numbers 7.4 Degenerate and Non-degenerate Orbitals 7.5 Degeneracy of Energy Levels 7.6 Wavefunction of The Hydrogen Atom 7.7 Calculation of Properties of Hydrogen Atom 7.8 Magnetic Properties: Angular Momentum and Magnetic Moment 7.9 Spin-Orbit Coupling and Term Symbols Chapter 8 Electronic Spectroscopy 8.1 Introduction 8.2 The Born-Oppenheimer Approximation for Electronic Spectra 8.3 Frank Codon Principle 8.4 Application of Electronic Spectroscopy to Organic Molecules 8.5 Electronic Excited State: Signlet and Triplet 8.6 Transition Dipole Moment 8.7 Selection Rules 8.8 Vibronic Coupling 8.9 Consequences of Light Absorption: The Jablonski Diagram Chapter 9 Multielectron System and Approximate Methods 9.1 Introduction 9.2 Pertubation Method 9.3 Variation Method 9.4 Self-Consistent Field Method Chapter 10 Chemical Bonding 10.1 Introduction 10.2 Born-Oppenheimer Approximation 10.3 Approximate Methods to Solve Schrödinger 10.4 Approximation of Linear Combination of Atomic Orbitals: LCAO-MO Treatment 10.5 LCAO-MO Treatment of Hydrogen Molecule Ion (H2 ) 10.6 Hydrogen Molecule: Qualitative Treatment 10.7 LCAO-MO Treatment of Hydrogen Molecule 10.8 Valence Bond Treatment (VBT) of Hydrogen Molecule 10.9 Comparison of VBT and MOT 10.10 LCAO-MO Treatment of Homonuclear Diatomic Molecules 10.11 LCAO-MO Treatment of Heteronuclear Diatomic Molecules 10.12 LCAO-MO Treatment of Triatomic Molecules Index
Chapter 1 Classical Mechanics 1.1 Dalton's Atomic Theory 1.2 What are Classical Mechanics and Quantum Mechanics? 1.3 J.J. Thomson Model of Atom 1.4 Rutherford's Nuclear Model of Atom - Discovery of Nucleus 1.5 Developments Leading to The Bohr Model of Atom 1.6 Bohr Model of Atom 1.7 Sommerfeld Theory or Bohr-Sommerfeld Theory Chapter 2 Towards Quantum Mechanics 2.1 Reasons for The Failure of Classical Model of Atom or Bohr Model of Atom 2.2 Developments Leading to Quantum Mechanical Model of Atom 2.3 De-Broglie's Dual Nature of Matter 2.4 Heisenberg's Uncertainty Principle Chapter 3 Introduction to Quantum Mechanics 3.1 Necessity of Quantum Mechanics 3.2 Schrodinger Wave Equation 3.3 Derivation of Time Independent Schrodinger Wave Equation 3.4 Physical Significance of Wavefunction ( ) and Probability Density ( ²) 3.5 Concept of Atomic Orbital 3.6 Quantum Mechanical Model of Atom 3.7 Eigen Value and Eigen Wavefunction 3.8 Normalised, Orthogonal and Orthonormal Wavefunction 3.9 Operators 3.10 Postulates of Quantum Mechanics 3.11 Derivation of Time Independent Schrodinger Wave Equation on The Basis of Postulates of Quantum Mechanics 3.12 Steady State Schrödinger Wave Equation Chapter 4 Particle in a Box: Quantisation of Translational Energy 4.1 Application of Postulates of Quantum Mechanics to Simple System 4.2 Operation of Quantum Mechanics 4.3 Introduction to Translational Motion of a Particle 4.4 Particle in One Dimensional Box: Quantisation of Translational Energy 4.5 Particle in Two-dimensional 4.6 Particle in Three Dimensional Box 4.7 Free Particle Chapter 5 Rigid Rotator and Rotational Spectra 5.1 Introduction 5.2 Classical Treatment of Rigid Rotator 5.3 Quantum Mechanical Treatment: Schrödinger Wave Equation for Rigid Rotator 5.4 Wavefunction of Rigid Rotator 5.5 Rotational Energy of the Rigid Rotator 5.6 Rotational Energy Levels 5.7 Rotational Selection Rules 5.8 Rotational Spectra of Rigid Diatomic Molecule 5.9 Microwave Active Molecules or Types of Molecules Showing Rotational Spectra 5.10 Parameters Calculated from Rotational Spectra 5.11 Isotopic Effect 5.12 Application of Microwave Radiation: Microwave Oven Chapter 6 Linear Harmonic Oscillator and Vibrational Spectra 6.1 Introduction 6.2 Classical Treatment of Linear Harmonic Oscillator 6.3 Quantum Mechanical Treatment: Schrödinger Wave Equation for Linear Harmonic Oscillator 6.4 Solution of Schrödinger Wave Equation: Vibrational Energy and Wavefunction of The Linear Harmonic Oscillator 6.5 Wavefunction Plots for Linear Harmonic Oscillator 6.6 Probability Plots for Linear Harmonic Oscillator 6.7 Symmetry of The Vibrational Wavefunction 6.8 Calculation of Properties of Linear Harmonic Oscillator 6.9 Orthonormal Sets of Wavefunction 6.10 Virial Theorem 6.11 Vibrational Energy and Zero Point Energy for Linear Harmonic Oscillator 6.12 Vibrational Selection Rule 6.13 Vibrational Spectra of Linear Harmonic Oscillator 6.14 Infrared Active Molecules or Types of Molecules Showing Vibrational Spectra Chapter 7 "Hydrogen Atom": Quantisation of Electronic Energy 7.1 Necessity of Replacing Bohr Theory 7.2 Setting of Schrodinger Equation for Hydrogen Atom 7.3 Quantum Numbers 7.4 Degenerate and Non-degenerate Orbitals 7.5 Degeneracy of Energy Levels 7.6 Wavefunction of The Hydrogen Atom 7.7 Calculation of Properties of Hydrogen Atom 7.8 Magnetic Properties: Angular Momentum and Magnetic Moment 7.9 Spin-Orbit Coupling and Term Symbols Chapter 8 Electronic Spectroscopy 8.1 Introduction 8.2 The Born-Oppenheimer Approximation for Electronic Spectra 8.3 Frank Codon Principle 8.4 Application of Electronic Spectroscopy to Organic Molecules 8.5 Electronic Excited State: Signlet and Triplet 8.6 Transition Dipole Moment 8.7 Selection Rules 8.8 Vibronic Coupling 8.9 Consequences of Light Absorption: The Jablonski Diagram Chapter 9 Multielectron System and Approximate Methods 9.1 Introduction 9.2 Pertubation Method 9.3 Variation Method 9.4 Self-Consistent Field Method Chapter 10 Chemical Bonding 10.1 Introduction 10.2 Born-Oppenheimer Approximation 10.3 Approximate Methods to Solve Schrödinger 10.4 Approximation of Linear Combination of Atomic Orbitals: LCAO-MO Treatment 10.5 LCAO-MO Treatment of Hydrogen Molecule Ion (H2 ) 10.6 Hydrogen Molecule: Qualitative Treatment 10.7 LCAO-MO Treatment of Hydrogen Molecule 10.8 Valence Bond Treatment (VBT) of Hydrogen Molecule 10.9 Comparison of VBT and MOT 10.10 LCAO-MO Treatment of Homonuclear Diatomic Molecules 10.11 LCAO-MO Treatment of Heteronuclear Diatomic Molecules 10.12 LCAO-MO Treatment of Triatomic Molecules Index
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