ONE FORMULA, ONE ANSWER
Quantum Harmonic Oscillator Energy Calculator
Calculate a one-dimensional quantum harmonic oscillator level including its zero-point energy. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Harmonic oscillator energy Eₙ
Enter values and select Calculate.
Eₙ = ℏω(n+1/2)
Assumptions
Required: ω>0 and nonnegative integer n. The potential is an ideal parabola with zero potential at equilibrium. Excluded: anharmonicity, damping, interactions and relativistic corrections. The input is angular frequency ω, related to frequency f in Hz by ω=2πf.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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