Index: Physics / Foundations

Physics — Foundations

Routing Summary

Core quantum mechanics: three survey notes (overview, formalism, phenomena) plus four atomic concept notes. Contains 7 notes. (The survey notes were consolidated here from the former Theoretical Physics/ folder on 2026-09-18.)

• Need the big picture of QM (history, wave functions, Schrödinger equation, worked examples)? → Quantum Mechanics - Overview
• Need the formalism in one place (Hilbert space, Hermitian observables, Born rule, composite systems)? → Quantum Mechanics - Mathematical Formalism
• Need the phenomena (wave-particle duality, double slit, tunneling, Bell’s theorem, decoherence)? → Quantum Mechanics - Key Phenomena
• Need the state postulate, Hilbert space and measurement in detail? → Wave Function and Hilbert Space
• Need time evolution and the Schrödinger equation? → Schrödinger Equation and Time Evolution
• Need the Heisenberg uncertainty principle? → Uncertainty Principle
• Need quantum entanglement and composite systems? → Quantum Entanglement

Concept Map

Concept	Note	Type	Depends On	Key Result
Wave functions, operators, Born rule, Schrödinger equation	Quantum Mechanics - Overview	overview	—	QM predicts probabilities, not certainties; states live in Hilbert space
Hilbert space, observables, uncertainty principle, entanglement	Quantum Mechanics - Mathematical Formalism	concept	Quantum Mechanics - Overview	Position and momentum cannot both be precisely known: ${\sigma }_X{\sigma }_P\ge \hslash /2$
Wave-particle duality, tunneling, double slit, Bell’s theorem	Quantum Mechanics - Key Phenomena	concept	Quantum Mechanics - Overview, Quantum Mechanics - Mathematical Formalism	No local hidden variable theory is consistent with experiment
Wave function & Hilbert space	Wave Function and Hilbert Space	definition	—	Quantum state as a normalized vector in $\mathcal{H}$; Born rule gives probabilities
Schrödinger equation	Schrödinger Equation and Time Evolution	theorem	Wave Function and Hilbert Space	$i\hslash {\partial }_t\psi =H\psi$; unitary evolution
Uncertainty principle	Uncertainty Principle	theorem	Wave Function and Hilbert Space	${\sigma }_X{\sigma }_P\ge \hslash /2$; canonical commutation
Quantum entanglement	Quantum Entanglement	concept	Wave Function and Hilbert Space	Non-separable joint states; Bell’s theorem rules out local hidden variables

Notes

• Quantum Mechanics - Overview — CONTAINS: QM historical development, wave functions, Schrödinger equation, time evolution, examples (free particle, harmonic oscillator)
• Quantum Mechanics - Mathematical Formalism — CONTAINS: Hilbert space formalism, observables as Hermitian operators, Born rule, uncertainty principle, composite systems, entanglement, Noether theorem in QM
• Quantum Mechanics - Key Phenomena — CONTAINS: wave-particle duality, double-slit experiment, quantum tunneling, quantum interference, Bell’s theorem, quantum entanglement, decoherence
• Wave Function and Hilbert Space — CONTAINS: quantum state postulate, Hilbert space, observables, Born rule, measurement collapse
• Schrödinger Equation and Time Evolution — CONTAINS: time-dependent Schrödinger eq., unitary evolution, free particle, particle in a box, stationary states
• Uncertainty Principle — CONTAINS: Heisenberg uncertainty, canonical commutation relations, position-momentum duality
• Quantum Entanglement — CONTAINS: tensor product Hilbert space, entangled states, Bell’s theorem, decoherence

Sources

• Quantum mechanics — Wikipedia: Quantum mechanics (2026-04-10)