Index: Physics / Foundations

Physics — Foundations

Routing Summary

Core quantum mechanics: the mathematical formalism, key postulates, and fundamental phenomena.

• Need the mathematical structure (Hilbert space, operators, Born rule)? → 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 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	$i\hslash {\partial }_t\psi =H\psi$; unitary evolution
Uncertainty principle	Uncertainty Principle	theorem	Wave Function	${\sigma }_X{\sigma }_P\ge \hslash /2$; canonical commutation
Quantum entanglement	Quantum Entanglement	concept	Wave Function	Non-separable joint states; Bell’s theorem rules out local hidden variables

Notes

• 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)