Atomic and Molecular Physics

Atomic and Molecular Physics is the branch of quantum physics that studies the structure and properties of atoms and simple molecules. It focuses on the arrangement of electrons and atomic nuclei and the processes by which these arrangements change, such as through interactions with each other or with electromagnetic radiation (light). This field provides the fundamental understanding of quantized energy levels, chemical bonding, and the absorption and emission of photons, which underpins modern spectroscopy, laser physics, and quantum chemistry.

1. Foundations of Quantum Mechanics
   1. Historical Development of Quantum Theory
      1. Classical Physics Limitations
      2. Blackbody Radiation Problem
      3. Planck's Quantum Hypothesis
      4. Planck Constant and Energy Quantization
      5. The Photoelectric Effect
      6. Einstein's Photon Theory
      7. Work Function and Threshold Frequency
      8. Compton Scattering
      9. Photon Momentum and Energy
      10. Compton Wavelength
      11. Wave-Particle Duality
      12. de Broglie Wavelength
      13. Matter Waves
      14. Double-Slit Experiment with Particles
      15. Early Atomic Models
      16. Thomson's Plum Pudding Model
      17. Rutherford's Nuclear Model
      18. The Bohr Model of the Atom
      19. Bohr's Postulates
      20. Quantized Angular Momentum
      21. Energy Levels and Spectral Lines
      22. Limitations of the Bohr Model
   2. Mathematical Foundations
      1. Complex Numbers in Quantum Mechanics
      2. Vector Spaces and Hilbert Spaces
      3. Linear Operators
      4. Hermitian Operators
      5. Commutators and Anticommutators
   3. The Schrödinger Equation
      1. Formulation and Motivation
      2. Time-Dependent Schrödinger Equation
      3. General Form and Structure
      4. Physical Interpretation
      5. Probability Current Density
      6. Continuity Equation
      7. Time-Independent Schrödinger Equation
      8. Separation of Variables Method
      9. Stationary States
      10. Bound States and Scattering States
      11. Energy Eigenvalue Problem
      12. Superposition Principle
      13. Linear Combinations of States
   4. Wavefunctions and Probability Interpretation
      1. Mathematical Properties of Wavefunctions
      2. Single-Valued and Continuous Requirements
      3. Square Integrability
      4. The Born Rule
      5. Probability Density Interpretation
      6. Measurement Postulates
      7. Normalization of Wavefunctions
      8. Normalization Condition
      9. Probability Conservation
      10. Global Phase Invariance
      11. Boundary Conditions
      12. Continuity Requirements
      13. Behavior at Infinity
   5. Quantum Mechanical Operators
      1. Definition and Properties
      2. Linear Operators
      3. Hermitian Operators
      4. Position Operator
      5. Representation in Position Space
      6. Eigenvalues and Eigenfunctions
      7. Momentum Operator
      8. Representation in Position Space
      9. Representation in Momentum Space
      10. Position-Momentum Commutation Relations
      11. Canonical Commutation Relations
      12. The Hamiltonian Operator
      13. Kinetic Energy Operator
      14. Potential Energy Operator
      15. Total Energy Eigenvalue Problem
      16. Eigenvalue Equations
      17. Physical Meaning of Eigenvalues
      18. Physical Meaning of Eigenfunctions
      19. Degeneracy
      20. Expectation Values
      21. Definition and Calculation
      22. Time Evolution of Expectation Values
      23. Ehrenfest's Theorem
   6. The Uncertainty Principle
      1. Heisenberg's Uncertainty Principle
      2. Position-Momentum Uncertainty Relation
      3. Energy-Time Uncertainty Relation
      4. Mathematical Derivation
      5. Commutation Relations and Uncertainty
      6. Generalized Uncertainty Principle
      7. Physical Implications and Examples
      8. Minimum Uncertainty States
      9. Coherent States
   7. Angular Momentum in Quantum Mechanics
      1. Classical Angular Momentum
      2. Orbital Angular Momentum Operators
      3. Definition in Cartesian Coordinates
      4. Angular Momentum Algebra
      5. Commutation Relations
      6. Fundamental Commutation Relations
      7. Angular Momentum Squared Operator
      8. Ladder Operators
      9. Raising and Lowering Operators
      10. Action on Angular Momentum States
      11. Eigenvalues and Eigenfunctions
      12. Quantization of Angular Momentum
      13. Quantum Numbers l and m
      14. Spherical Harmonics
      15. Definition and Properties
      16. Orthogonality and Completeness
      17. Applications in Central Potentials
      18. Spin Angular Momentum
      19. Intrinsic Angular Momentum
      20. Spin Operators and Algebra
      21. Spin-1/2 Systems
      22. Pauli Matrices
      23. Spinor Wavefunctions
      24. Addition of Angular Momenta
      25. Clebsch-Gordan Coefficients
      26. Total Angular Momentum