quantum harmonic oscillator

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb: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
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 gptkb:Susskind–Glogower_phase_operators
gptkbp:bfsLayer	5
https://www.w3.org/2000/01/rdf-schema#label	quantum harmonic oscillator