Quantum Mechanics

Quantum Mechanics is the fundamental theory in physics that provides the mathematical framework for describing the behavior of nature at the scale of atoms and subatomic particles. As the foundation of all quantum physics, it departs from classical mechanics by introducing concepts such as quantization, where physical properties exist in discrete units; wave-particle duality, the principle that particles can exhibit both wave and particle characteristics; and the uncertainty principle, which sets a fundamental limit on the precision with which pairs of properties like position and momentum can be known. The theory is inherently probabilistic, using the Schrödinger equation to calculate the likelihood of an outcome rather than a deterministic result.

1. Historical Development and Foundations
   1. Classical Physics Limitations
      1. Mechanical Systems
         1. Deterministic Motion
         2. Continuous Energy
         3. Predictability Assumptions
      2. Electromagnetic Theory
         1. Maxwell's Equations
         2. Wave Theory of Light
         3. Classical Radiation Theory
      3. Thermodynamics and Statistical Mechanics
         1. Equipartition Theorem
         2. Classical Statistical Distributions
   2. Experimental Crises
      1. Black-Body Radiation Problem
         1. Experimental Observations
         2. Rayleigh-Jeans Law
         3. Ultraviolet Catastrophe
         4. Planck's Solution
         5. Energy Quantization Hypothesis
         6. Planck's Constant
         7. Planck Distribution Law
      2. Photoelectric Effect
         1. Experimental Setup and Observations
         2. Threshold Frequency Phenomenon
         3. Intensity Independence
         4. Einstein's Photon Theory
         5. Work Function Concept
         6. Energy Conservation in Photoemission
      3. Compton Scattering
         1. X-ray Scattering Experiments
         2. Wavelength Shift Observations
         3. Particle Model of Photons
         4. Compton Formula Derivation
         5. Momentum Conservation
      4. Atomic Spectra
         1. Line Spectra Observations
         2. Hydrogen Spectrum
         3. Rydberg Formula
         4. Spectral Series
   3. Early Quantum Models
      1. Bohr Atomic Model
         1. Postulates of Quantization
         2. Circular Orbits
         3. Angular Momentum Quantization
         4. Energy Level Formula
         5. Successes and Limitations
      2. Sommerfeld Extensions
         1. Elliptical Orbits
         2. Relativistic Corrections
         3. Fine Structure
   4. Wave-Particle Duality
      1. De Broglie Matter Waves
         1. Matter Wave Hypothesis
         2. De Broglie Wavelength
         3. Momentum-Wavelength Relation
      2. Experimental Confirmations
         1. Davisson-Germer Experiment
         2. Electron Diffraction
         3. Double-Slit Experiments
         4. Complementarity Principle