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The 40 pages that link to Quantum harmonic oscillator, each with the reason it gives.

• PhotonRelated: Each electromagnetic field mode behaves mathematically like a quantum oscillator.

• Raman spectroscopyRelated: It approximates vibrational energy levels used to interpret Raman transitions.

• PhononRelated: A lattice's independent vibrational modes behave as quantum harmonic oscillators.

• Molecular vibrationRelated: It explains discrete vibrational energy levels in the harmonic approximation.

• Vibrational spectroscopyRelated: Its quantized levels explain why spectra show discrete vibrational transitions.

• Quantum opticsRelated: Each mode of the electromagnetic field behaves mathematically like a quantum harmonic oscillator.

• Canonical commutation relationRelated: Its ladder-operator solution relies on the canonical position–momentum algebra.

• Quantum fieldRelated: Each independent field mode behaves mathematically like a quantum harmonic oscillator.

• Sturm–Liouville theoryRelated: Its bound-state equation is a solvable eigenvalue problem with orthogonal eigenfunctions.

• Vacuum energyRelated: Each field mode behaves like an oscillator with a nonzero ground-state energy.

• Degenerate energy levelsRelated: Higher-dimensional versions have multiple states at the same total excitation energy.

• Position operatorRelated: Its position operator connects energy eigenstates to spatial motion and observables.

• Quantum potentialRelated: Its stationary ground state provides a case where the quantum potential offsets classical confinement.

• Planck postulateRelated: Its evenly spaced energy levels clarify a modern oscillator-based account of quantization.