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quantum harmonic oscillator
URI:
https://gptkb.org/entity/quantum_harmonic_oscillator
GPTKB entity
Statements (31)
Predicate
Object
gptkbp:instanceOf
quantum mechanical system
gptkbp:commutationRelation
[a, a†] = 1
gptkbp:describes
particle in a quadratic potential
gptkbp:energyLevelFormula
E_n = (n + 1/2)ħω
gptkbp:hasAnnihilationOperator
a
gptkbp:hasApplication
gptkb:quantum_field_theory
molecular spectroscopy
quantum optics
solid state physics
gptkbp:hasCreationOperator
a†
gptkbp:hasEnergyLevels
discrete
gptkbp:hasEquallySpacedLevels
yes
gptkbp:hasExcitedStates
n = 1, 2, 3, ...
gptkbp:hasGroundStateEnergy
1/2 ħω
gptkbp:hasHamiltonian
H = (p^2/2m) + (1/2)mω^2x^2
gptkbp:hasLadderOperators
yes
gptkbp:hasModel
quantized electromagnetic field
phonons in solids
vibrational modes in molecules
gptkbp:hasWavefunctions
gptkb:Hermite_polynomials
gptkbp:hasZeroPointEnergy
yes
https://www.w3.org/2000/01/rdf-schema#label
quantum harmonic oscillator
gptkbp:isExactlySolvable
yes
gptkbp:solvedBy
gptkb:Schrödinger_equation
gptkbp:symmetry
parity
gptkbp:usedIn
gptkb:statistical_mechanics
gptkb:quantum_computing
gptkb:quantum_information_theory
quantum chemistry
gptkbp:bfsParent
gptkb:quantum_physics
gptkbp:bfsLayer
4