Part II: Foundations of Quantum Mechanics
From the historical origins through Planck, Einstein, and Bohr, to the modern postulates of quantum mechanics. We explore wave functions, measurement, uncertainty, and the profound conceptual shifts that quantum theory demands.
Part Overview
Quantum mechanics revolutionized physics in the early 20th century. Unlike classical mechanics, quantum theory introduces probability, wave-particle duality, and the observer's fundamental role in measurements. This part establishes the conceptual and mathematical foundations.
Key Topics
- • Black-body radiation, photoelectric effect, Bohr atom
- • Postulates of quantum mechanics
- • Wave functions and probability interpretation
- • Measurement and wavefunction collapse
- • Heisenberg uncertainty principle
- • Superposition and quantum interference
- • Copenhagen, Many-Worlds, and other interpretations
60+ pages | 8 chapters | Core conceptual foundations
Chapters
Chapter 1: Historical Development
Black-body radiation, Planck's quantum hypothesis, photoelectric effect, Compton scattering, Bohr model, de Broglie waves, and the old quantum theory.
Chapter 2: Postulates of QM
States as vectors, observables as operators, measurement postulate, time evolution (Schrödinger equation), and composite systems.
Chapter 3: Wave Functions
Position and momentum representations, probability density, normalization, expectation values, and the Schrödinger equation in position space.
Chapter 4: Measurement & Collapse
The measurement problem, wavefunction collapse, Born rule, projection postulate, compatible and incompatible observables, and measurement back-action.
Chapter 5: Uncertainty Principle
Heisenberg uncertainty relation, generalized uncertainty, proof via Cauchy-Schwarz, energy-time uncertainty, and physical implications.
Chapter 6: Superposition & Interference
Linear superposition, double-slit experiment, quantum interference, coherence, and the principle of complementarity.
Chapter 7: Correspondence Principle
Classical limit of quantum mechanics, Ehrenfest theorem, WKB approximation revisited, and connection to classical physics.
Chapter 8: Interpretations of QM
Copenhagen interpretation, Many-Worlds, de Broglie-Bohm pilot wave, consistent histories, and ongoing debates about quantum reality.