Harmonic oscillator: Calculate the ground state energy of a harmonic oscillator with a classical frequency of 3.68 × 10¹⁵ Hz. (1 eV = 1.60 × 10^-19 J, ħ = 1.055 × 10^-34 J ∙ s, h = 6.626 × 10^-34 J ∙ s) A) 7.62 eV B) 15.2 eV C) 11.4 eV D) 5.71 eV

Question

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The ground state energy of a harmonic oscillator is given by E = (1/2)ħω, where ω = 2πf. Substituting the given values, E = (1/2)(1.055 × 10^-34 J∙s)(2π)(3.68 × 10^15 Hz) = 1.22 × 10^-18 J. Converting to eV: 1.22 × 10^-18 J / 1.60 × 10^-19 J/eV = 7.62 eV.

Harmonic Oscillator: Calculate the Ground State Energy of a Harmonic