List of mathematical topics in quantum theory

This is a list of mathematical topics in quantum theory, by Wikipedia page. See also list of functional analysis topics, list of Lie group topics, list of quantum-mechanical systems with analytical solutions.

Mathematical formulation of quantum mechanics

 * bra–ket notation
 * canonical commutation relation
 * complete set of commuting observables
 * Heisenberg picture
 * Hilbert space
 * Interaction picture
 * Measurement in quantum mechanics
 * quantum field theory
 * quantum logic
 * quantum operation
 * Schrödinger picture
 * semiclassical
 * statistical ensemble
 * wavefunction
 * wave–particle duality
 * Wightman axioms
 * WKB approximation

Schrödinger equation

 * quantum mechanics, matrix mechanics, Hamiltonian (quantum mechanics)
 * particle in a box
 * particle in a ring
 * particle in a spherically symmetric potential
 * quantum harmonic oscillator
 * hydrogen atom
 * ring wave guide
 * particle in a one-dimensional lattice (periodic potential)
 * Fock symmetry in theory of hydrogen

Symmetry

 * identical particles
 * angular momentum
 * angular momentum operator
 * rotational invariance
 * rotational symmetry
 * rotation operator
 * translational symmetry
 * Lorentz symmetry
 * Parity transformation
 * Noether's theorem
 * Noether charge
 * Spin (physics)
 * isospin
 * Aman matrices
 * scale invariance
 * spontaneous symmetry breaking
 * supersymmetry breaking

Quantum states

 * quantum number
 * Pauli exclusion principle
 * quantum indeterminacy
 * uncertainty principle
 * wavefunction collapse
 * zero-point energy
 * bound state
 * coherent state
 * squeezed coherent state
 * density state
 * Fock state, Fock space
 * vacuum state
 * quasinormal mode
 * no-cloning theorem
 * quantum entanglement

Dirac equation

 * spinor, spinor group, spinor bundle
 * Dirac sea
 * Spin foam
 * Poincaré group
 * gamma matrices
 * Dirac adjoint
 * Wigner's classification
 * anyon

Interpretations of quantum mechanics

 * Copenhagen interpretation
 * locality principle
 * Bell's theorem
 * Bell test loopholes
 * CHSH inequality
 * hidden variable theory
 * path integral formulation, quantum action
 * Bohm interpretation
 * many-worlds interpretation
 * Tsirelson's bound

Quantum field theory

 * Feynman diagram
 * One-loop Feynman diagram
 * Schwinger's quantum action principle
 * Propagator
 * Annihilation operator
 * S-matrix
 * Standard Model
 * Local quantum physics
 * Nonlocal
 * Effective field theory
 * Correlation function (quantum field theory)
 * Renormalizable
 * Cutoff
 * Infrared divergence, infrared fixed point
 * Ultraviolet divergence
 * Fermi's interaction
 * Path-ordering
 * Landau pole
 * Higgs mechanism
 * Wilson line
 * Wilson loop
 * Tadpole (physics)
 * Lattice gauge theory
 * BRST charge
 * Anomaly (physics)
 * Chiral anomaly
 * Braid statistics
 * Plekton

Computation

 * quantum computing
 * qubit
 * qutrit
 * pure qubit state
 * quantum dot
 * Kane quantum computer
 * quantum cryptography
 * quantum decoherence
 * quantum circuit
 * universal quantum computer
 * measurement based Quantum Computing
 * timeline of quantum computing

Supersymmetry

 * Lie superalgebra
 * supergroup (physics)
 * supercharge
 * supermultiplet
 * supergravity

Quantum gravity

 * theory of everything
 * loop quantum gravity
 * spin network
 * black hole thermodynamics

Non-commutative geometry

 * Quantum group
 * Hopf algebra
 * Noncommutative quantum field theory

String theory
See list of string theory topics


 * Matrix model