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The 169 pages that link to Quantum mechanics, each with the reason it gives.

• SpectroscopyNarrower topic: Its quantized states account for many discrete spectral features.

• Albert EinsteinCompared with: Einstein helped establish quantum ideas but objected to their standard probabilistic interpretation.

• ElectronNarrower topic: Electron states and measurements follow quantum rather than classical rules.

• Quantum field theoryNarrower topic: Quantum field theory extends its quantum principles to fields and particle-changing processes.

• Statistical mechanicsRelated: Quantum statistical mechanics counts quantum states and accounts for indistinguishable particles.

• Newton's laws of motionCompared with: Newton's laws do not describe microscopic systems with quantum behavior.

• Complex numberRelated: Quantum state amplitudes are complex numbers whose squared magnitudes yield probabilities.

• Quantum electrodynamicsNarrower topic: QED extends quantum mechanics to fields and relativistic particle creation.

• Niels BohrNarrower topic: Bohr’s early model helped lead toward the broader theory that superseded it.

• Classical mechanicsCompared with: Quantum mechanics is needed when classical predictions fail at microscopic scales.

• Hilbert spaceRelated: Quantum state vectors occupy Hilbert spaces, with inner products encoding probability amplitudes.

• Hamiltonian mechanicsCompared with: Canonical variables and Poisson brackets have quantum counterparts, but classical phase-space motion is replaced.

• Partial differential equationRelated: The Schrödinger equation is a PDE governing quantum-state evolution.

• Celestial mechanicsCompared with: It governs microscopic phenomena, unlike the classical gravitational motion usually modeled here.

• Quantum gravityNarrower topic: Any quantum theory of gravity must preserve quantum principles such as superposition.

• Newtonian mechanicsCompared with: Newtonian trajectories fail to describe many microscopic phenomena.

• Planck constantNarrower topic: The Planck constant sets the scale of this broader framework’s characteristic effects.

• Thermal radiationNarrower topic: Quantization introduced to explain thermal spectra became foundational to this broader theory.

• Nuclear magnetic resonanceNarrower topic: Quantized nuclear spin states explain NMR energy levels and resonance transitions.

• Linear algebraRelated: Quantum states are represented by vectors, and observables by linear operators.

• Hydrogen atomNarrower topic: Hydrogen’s bound states require a quantum description, not classical orbits.

• Quantum computingNarrower topic: Quantum computing relies on the theory’s rules for states, operations, and measurement.

• Nuclear physicsNarrower topic: Nuclear models rely on its principles to describe quantized nuclear states and reactions.

• Dirac equationNarrower topic: The Dirac equation applies quantum wave dynamics to relativistic particles.

• DeterminismRelated: Standard interpretations assign fundamental probabilities to measurement outcomes, challenging classical determinism.

• Astronomical spectroscopyNarrower topic: Quantized energy levels explain why atoms produce discrete spectral lines.

• Representation theoryRelated: Representations model symmetries acting on quantum state spaces and classify possible particle states.

• Bell's theoremNarrower topic: Bell's theorem compares local models with its predicted correlations.

• Molecular spectroscopyNarrower topic: Quantized molecular states make spectroscopy's discrete transitions possible.

• Werner HeisenbergNarrower topic: Heisenberg helped establish this framework by replacing classical trajectories with quantum observables.

• Euler's formulaRelated: Complex phases in quantum amplitudes are naturally expressed with exponentials.

• Quantum chemistryNarrower topic: Quantum chemistry applies this broader theory to chemical systems.

• Max BornNarrower topic: Born’s interpretation helped establish the modern probabilistic framework of the theory.

• Complex exponentialRelated: Time evolution commonly includes complex exponential phase factors.

• OrthogonalityRelated: Orthogonal state vectors represent perfectly distinguishable quantum states.

• Wolfgang PauliNarrower topic: Pauli helped establish its formal structure and interpret its rules.

• Atomic spectrumNarrower topic: Its rules account for discrete atomic states and the transitions that generate spectra.

• Georges LemaîtreRelated: Lemaître drew on ideas about atomic disintegration when imagining cosmic beginnings.

• Gustav KirchhoffRelated: The blackbody-radiation problem associated with Kirchhoff’s work became a key route toward quantum theory.

• Paul DiracNarrower topic: Dirac developed a general mathematical framework for quantum states and observables.

• Wave–particle dualityNarrower topic: Wave–particle duality is a central feature of its account of measurement and behavior.

• AstrophysicsRelated: It explains the atomic transitions and particle behavior that shape stellar spectra and dense matter.

• Group representationRelated: Symmetry operators on quantum states form group representations.

• J. Robert OppenheimerNarrower topic: Oppenheimer’s early research applied this framework to atoms and molecules.

• Atomic spectroscopyNarrower topic: Its rules determine the discrete states and radiation transitions measured in atomic spectra.

• George GamowNarrower topic: Gamow’s early work on alpha decay applied quantum mechanics to a nuclear problem.

• Mathematical physicsBroader topic: Its formalism draws on Hilbert spaces, operators, and spectral theory.

• Old quantum theoryNarrower topic: It replaced the old framework with a consistent formalism for microscopic systems.

• Path integral formulationNarrower topic: The path integral is an alternative formulation of this broader theory.

• William ShockleyNarrower topic: Shockley’s semiconductor research relied on quantum explanations of electrons in solids.