Quantum Harmonic Oscillator Calculator
Energy levels, zero-point energy, level spacing and classical turning points of a quantum harmonic oscillator.
How to use the Quantum Harmonic Oscillator Calculator
- Enter or select: Particle, Spring constant k, Quantum number n.
- Fill in what you know of: Custom mass — leave the unknown empty.
- The results (Angular frequency ω, Frequency, Energy Eₙ, Zero-point energy, Level spacing ħω, Transition wavelength, Classical turning point) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- Eₙ = ħω(n + ½)
- ω = √(k/m)
- x_turn = √((2n+1)ħ/(mω))