External

Introduction to Quantum Mechanics

Chemistry

Author: Kristie Koski
Publisher: University of California, Davis
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 106 sections

01: The Dawn of the Quantum Theory
1.01: Blackbody Radiation Cannot Be Explained Classically
1.02: Quantum Hypothesis used for Blackbody Radiation Law
1.03: Photoelectric Effect Explained with Quantum Hypothesis
1.04: The Hydrogen Atomic Spectrum
1.05: The Rydberg Formula and the Hydrogen Atomic Spectrum
1.06: Matter Has Wavelike Properties
1.07: de Broglie Waves can be Experimentally Observed
1.08: The Bohr Theory of the Hydrogen Atom
1.09: The Heisenberg Uncertainty Principle
1.10: The Dawn of the Quantum Theory (Exercises)
02: The Classical Wave Equation
2.1: The One-Dimensional Wave Equation
2.2: The Method of Separation of Variables
2.3: Oscillatory Solutions to Differential Equations
2.4: The General Solution is a Superposition of Normal Modes
2.5: A Vibrating Membrane
2.6: The Classical Wave Equation (Exercises)
03: The Schrodinger Equation
3.01: The Schrodinger Equation
3.02: Linear Operators in Quantum Mechanics
3.03: The Schrodinger Equation is an Eigenvalue Problem
3.04: The Quantum Mechanical Free Particle
3.05: Wavefunctions Have a Probabilistic Interpretation
3.06: The Energy of a Particle in a Box is Quantized
3.07: Wavefunctions Must Be Normalized
3.08: The Average Momentum of a Particle in a Box is Zero
3.09: Particle in a Finite Box and Tunneling (optional)
3.10: The Uncertainty Principle Redux - Estimating Uncertainties from Wavefunctions
3.11: A Particle in a Two-Dimensional Box
3.12: A Particle in a Three-Dimensional Box
3.13: The Schrodinger Equation and a Particle in a Box (Exercises)
04: Postulates and Principles of Quantum Mechanics
4.1: The Wavefunction Specifies the State of a System
4.2: Quantum Operators Represent Classical Variables
4.3: Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
4.4: The Time-Dependent Schrodinger Equation
4.5: The Eigenfunctions of Operators are Orthogonal
4.6: Heisenburg Uncertainy Principle III - Commuting Operators
4.7: Postulates and Principles of Quantum Mechanics (Exercises)
05: The Harmonic Oscillator and the Rigid Rotor
5.01: A Harmonic Oscillator Obeys Hooke's Law
5.02: The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
5.03: The Harmonic Oscillator is an Approximation
5.04: The Harmonic Oscillator Energy Levels
5.05: The Harmonic Oscillator and Infrared Spectra
5.06: The Harmonic-Oscillator Wavefunctions Involve Hermite Polynomials
5.07: Hermite Polynomials are either Even or Odd Functions
5.08: The Energy Levels of a Rigid Rotor
5.09: The Rigid Rotator is a Model for a Rotating Diatomic Molecule
5.10: The Harmonic Oscillator and the Rigid Rotor (Exercises)
06: The Hydrogen Atom
6.1: The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
6.2: The Wavefunctions of a Rigid Rotator are Called Spherical Harmonics
6.3: The Three Components of Angular Momentum Cannot be Measured Simultaneously with Arbitrary Precision
6.4: Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
6.5: s Orbitals are Spherically Symmetric
6.6: Orbital Angular Momentum and the p-orbitals
6.7: The Helium Atom Cannot Be Solved Exactly
6.8: The Hydrogen Atom (Exercises)
07: Approximation Methods
7.1: Slater's Rules for Shielding
7.2: The Variational Method
7.3: Linear Variational Method and the Secular Determinant
7.4: Trial Functions Can Be Linear Combinations of Functions with Variational Parameters
7.5: Perturbation Theory Expresses the Solutions in Terms of Solved Problems
7.6: Approximation Methods (Exercises)
08: Multielectron Atoms
8.01: Atomic and Molecular Calculations are Expressed in Atomic Units
8.02: Perturbation Theory and the Variational Method for Helium
8.03: Hartree-Fock Equations are Solved by the Self-Consistent Field Method
8.04: An Electron Has An Intrinsic Spin Angular Momentum
8.05: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons
8.06: Antisymmetric Wave Functions can be Represented by Slater Determinants
8.07: Hartree-Fock Calculations Give Good Agreement with Experimental Data
8.08: Term Symbols Gives Detailed Descriptions of an Electron Configuration
8.09: Multi-electron Considerations - A Closer Look at Helium
8.10: The Allowed Values of J - the Total Angular Momentum Quantum Number
8.11: Hund's Rules Determine the Term Symbols of the Ground Electronic States
8.12: Using Atomic Term Symbols to Describe Atomic Spectra
8.13: Multielectron Atoms (Exercises)
09: The Chemical Bond: Diatomic Molecules
9.01: The Born-Oppenheimer Approximation Simplifies the Molecular Schrodinger Equation
9.02: The H Prototypical Species
9.03: Solving the H System Exactly (Optional)
9.04: The Overlap Integral
9.05: Evaluating the Overlap Integral (Optional)
9.06: Chemical Bond Stability
9.07: Bonding and Antibonding Orbitals
9.08: A Simple Molecular-Orbital Treatment of H Places Both Electrons in a Bonding Orbital
9.09: Molecular Orbitals Can Be Ordered According to Their Energies
9.10: Molecular-Orbital Theory Does not Predict a Stable Diatomic Helium Molecule
9.11: Electrons Populate Molecular Orbitals According to the Pauli Exclusion Principle
9.12: Molecular Orbital Theory Predicts that Molecular Oxygen is Paramagnetic
9.13: The Chemical Bond: Diatomic Molecules (Exercises)
10: MathChapters
10.01: Complex Numbers
10.02: Probability and Statistics
10.03: Vectors
10.04: Spherical Coordinates
10.05: Determinants
10.06: Matrices
10.07: Numerical Methods
10.08: Partial Differentiation
10.09: Series and Limits
10.10: The Binomial Distribution and Stirling's Appromixation