Keyword Glossary

Click a keyword to see every lesson that uses it.

All keywordsAdjointAdjoint operatorAlgebra B(H)Algebraic dualAtlasAtomic beamBell inequalitiesBorn ruleBounded operatorsBounded setsCanonical commutationCauchy sequencesClosureCompact setsCompletenessContinuityContinuous spectrumDaggerDeficiency indicesDense domainDensityDirac deltaDirac notationDiscrete spectrumEhrenfest theoremFourier transformFunctional calculusHilbert basisHilbert dimensionHilbert spacesInfinite dimensionInhomogeneous magnetic fieldInner productsIsomorphismsKets and brasLarmor precessionLinear operatorsMagnetic momentMatrix elementsModel spacesMomentum operatorMomentum representationNormal operatorsNormsOperator compositionOperator domainOperator normPosition operatorPosition representationPostulatesPre-Hilbert spacesQuantizationQuantum entanglementQuantum measurementReference sheetResolution of identityResolution of the identityResolventRiesz isomorphismSchrodinger equationSelf-adjoint extensionsSelf-adjointnessSpectral measureSpectral propertiesSpectral theoremSpectrumSpinSpin componentsState projectionStern-GerlachStrong convergenceStrong topologySuperpositionSymmetric operatorsTopological dualUnbounded operatorsUnitary evolutionUnitary operatorsVector spacesVector subspacesWavefunction collapseWeak convergenceWeak topology

Adjoint

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator Theory

Adjoint operator

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Algebra B(H)

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded Operators

Algebraic dual

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Atlas

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Atlas of Linear Operators

Atomic beam

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Bell inequalities

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Born rule

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Bounded operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded Operators

Bounded sets

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Canonical commutation

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Cauchy sequences

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Closure

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Compact sets

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Completeness

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert SpacesTheme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Continuity

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator Theory

Continuous spectrum

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Dagger

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Deficiency indices

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Dense domain

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator TheoryTheme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Density

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Dirac delta

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Dirac notation

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite DimensionTheme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Dirac Reference Sheet

Discrete spectrum

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Ehrenfest theorem

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Fourier transform

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Functional calculus

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Hilbert basis

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Hilbert dimension

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Hilbert spaces

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Infinite dimension

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Inhomogeneous magnetic field

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Inner products

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Isomorphisms

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Kets and bras

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Larmor precession

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Linear operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator TheoryTheme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Atlas of Linear Operators

Magnetic moment

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Matrix elements

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Model spaces

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Momentum operator

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Momentum representation

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Normal operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded Operators

Norms

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Operator composition

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator Theory

Operator domain

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator Theory

Operator norm

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 4: Linear Operator Theory

Position operator

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Position representation

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Postulates

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Pre-Hilbert spaces

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Quantization

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Quantum entanglement

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Quantum measurement

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach ExperimentTheme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Reference sheet

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Dirac Reference Sheet

Resolution of identity

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 5: Dirac Notation — Infinite Dimension

Resolution of the identity

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Resolvent

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Riesz isomorphism

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Schrodinger equation

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Self-adjoint extensions

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Self-adjointness

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded Operators

Spectral measure

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Spectral properties

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Atlas of Linear Operators

Spectral theorem

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded OperatorsTheme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Spectrum

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 8: Spectral Theory

Spin

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Spin components

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

State projection

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Stern-Gerlach

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Theme 1 (General Introduction and Foundational Experiments) - Lesson 1: Stern-Gerlach Experiment

Strong convergence

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Strong topology

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Superposition

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Symmetric operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Topological dual

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 2: Dual Space, Kets, Bras, Adjoint

Unbounded operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 7: Unbounded Operators

Unitary evolution

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Unitary operators

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 6: Bounded Operators

Vector spaces

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 1: Hilbert Spaces

Vector subspaces

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Wavefunction collapse

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Theme 3 (Postulates) - Lesson 1: Measurement, Dynamics, and Interpretation

Weak convergence

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces

Weak topology

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Theme 2 (Hilbert Spaces and Linear Operators) - Lesson 3: Topology of Hilbert Spaces