Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
The framework governing physical systems whose states exhibit superposition, probabilistic measurement outcomes, and noncommuting observables.
States are represented in a complex Hilbert space, observables by operators, and isolated-system evolution by unitary dynamics.
Nonrelativistic quantum mechanics is an effective framework; relativistic particle creation and annihilation require quantum field theory.
wp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsnist-quantum-theorytong-quantumEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Planck’s quantized energy elements solved the blackbody problem and initiated the quantum developments that culminated in quantum mechanics.
The source experiment, observation, anomaly, or problem materially motivated the development, revision, or acceptance of the target concept. Historical influence is not logical derivation; the edge detail states the documented role and avoids retrospective origin myths.
wp-physics-blackbody_ultraviolet_catastrophenist-blackbodyThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics is ordinarily formulated over complex vector spaces.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-physics-quantum_mechanicsnlab-physics-quantum_mechanicswp-complex_vector_spacenlab-complex_vector_spaceThis is an authored directed relation from the source endpoint to the target endpoint.
Standard quantum mechanics represents pure states by rays in a complex Hilbert space and observables by operators acting on it.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
nist-quantum-theorywp-physics-quantum_mechanicsnlab-physics-quantum_mechanicswp-hilbertnlab-hilbertThis is an authored directed relation from the source endpoint to the target endpoint.
The photoelectric effect was a central anomaly motivating quantum descriptions of radiation and matter.
The source experiment, observation, anomaly, or problem materially motivated the development, revision, or acceptance of the target concept. Historical influence is not logical derivation; the edge detail states the documented role and avoids retrospective origin myths.
wp-physics-photoelectric_effect_experimentsnobel-photoelectricnist-historical-constantsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics specializes physical theory to systems requiring quantum states, amplitudes, and probabilistic measurement rules.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
nist-quantum-theorywp-physics-quantum_mechanicsnlab-physics-quantum_mechanicswp-physics-physical_theorynlab-physics-physical_theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The Schrödinger equation supplies the state-evolution law for the Schrödinger-picture formulation of nonrelativistic quantum mechanics; it is not the universal evolution equation of all quantum theories.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-schrodinger_equationnlab-physics-schrodinger_equationwp-physics-quantum_mechanicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The phase shift agrees with quantum minimal coupling and cannot be represented solely by the local magnetic field along the particle paths.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-aharonov_bohm_interference_experimentsaharonov-bohm-experimentThis is an authored directed relation from the source endpoint to the target endpoint.
Successive Bell tests, including loophole-reduced and loophole-free implementations, support quantum predictions.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-bell_test_experimentsnobel-bell-testsaps-loophole-free-bellThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics permits entangled-state measurement correlations that violate Bell inequalities. Not every entangled state violates a Bell inequality, so entanglement alone is not the theorem premise.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
nist-quantum-theoryhorodecki-entanglement-reviewThis is an authored directed relation from the source endpoint to the target endpoint.
The Bohr model is a semiclassical approximation superseded by wave mechanics.
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
wp-physics-bohr_modelnist-hydrogenwp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum Hamiltonians may have normalizable bound states.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-bound_statenlab-physics-bound_statewp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Nonrelativistic many-body quantum mechanics with electromagnetic interactions explains molecular binding surfaces and bond-dependent spectra, with relativistic and QED corrections needed at higher precision or nuclear charge.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
wp-physics-chemical-bondiupac-chemical-bondnist-quantum-theorywp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Classical behavior emerges in suitable large-action, narrow-wavepacket, coarse-grained, and environmentally decohered regimes; no single universal limit covers all quantum systems.
The target is a collective, organizational, or scale-dependent phenomenon of the source constituents and interactions; it is not a mere list or classical sum of constituents.
tong-quantumschlosshauer-decoherence-2019This is an authored directed relation from the source endpoint to the target endpoint.
The result supported quantum kinematics beyond classical wave scattering.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-compton_scattering_experimentnobel-comptonThis is an authored directed relation from the source endpoint to the target endpoint.
The diffraction peaks agreed with de Broglie wavelengths and quantum wave mechanics.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-davisson_germer_experimentaps-davisson-germerThis is an authored directed relation from the source endpoint to the target endpoint.
Many-body quantum mechanics specializes quantum theory to interacting multi-degree systems.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-many_body_quantum_mechanicsnlab-physics-many_body_quantum_mechanicswp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Molecular electronic, vibrational, and rotational states are quantum mechanical; practical calculations use controlled approximations such as Born–Oppenheimer separation.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
iupac-moleculenist-quantum-theorywp-physics-moleculewp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Nonrelativistic quantum mechanics specializes quantum theory to low velocities and fixed particle number.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum chemistry specializes quantum mechanics to electronic structure, molecular geometry, spectra, and reactivity using explicit Hamiltonians and controlled or empirical approximations.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-quantum_mechanicstong-quantumwp-chem-quantum-chemistryopenstax-chemistry-2eThis is an authored directed relation from the source endpoint to the target endpoint.
QFT incorporates quantum states, observables, amplitudes, and probabilistic prediction while allowing fields and variable particle number.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-quantum_field_theorynlab-physics-quantum_field_theorywp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
The harmonic oscillator is the universal quadratic quantum model near stable equilibria and for free field modes.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-quantum_harmonic_oscillatornlab-physics-quantum_harmonic_oscillatorwp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics represents observables by operators or generalized measurements.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
nist-quantum-theorywp-physics-observablenlab-physics-quantum_observablewp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Perturbation theory expands around a solvable Hamiltonian in a controlled small parameter when convergence or asymptotic accuracy permits.
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
wp-physics-quantum_perturbation_theorytong-quantumwp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics represents the state of a system by a state vector, ray, or density operator.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
nist-quantum-theorywp-physics-quantum_statenlab-physics-quantum_statewp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics supplies the state spaces, observables, and microscopic evolution used in quantum statistical mechanics; statistical ensembles and thermodynamic limits add structure beyond ordinary single-system quantum theory.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-quantum_mechanicswp-physics-quantum-statistical-mechanicstong-statistical-physicsThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics governs quantum systems in its domain.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
wp-physics-quantum_mechanicsnlab-physics-quantum_mechanicswp-physics-quantum_systemnlab-physics-quantum_systemThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum mechanics assigns amplitudes across potential barriers rather than enforcing a classical turning point; observable tunneling rates depend on the system, environment, and boundary conditions.
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
tong-quantumThis is an authored directed relation from the source endpoint to the target endpoint.
Quantum Hamiltonians may have continuum scattering states.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-scattering_statewp-physics-quantum_mechanicsnlab-physics-quantum_mechanicsThis is an authored directed relation from the source endpoint to the target endpoint.
Modern quantum mechanics accounts for the two-valued spin measurement of the silver valence electron.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-stern_gerlach_experimentaps-stern-gerlachThis is an authored directed relation from the source endpoint to the target endpoint.
The variational method restricts the state search to a parameterized family and optimizes the energy.
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
wp-physics-variational_methodtong-quantumwp-physics-quantum_mechanicsnlab-physics-quantum_mechanics