// multi-utility computation suite · offline · instant · precise
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│ [c] calcalyst_ │
│ computation suite │
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sci.quantum-harmonic-oscillator-energy Calculator
Calculates quantum harmonic oscillator energy levels E_n = ℏω(n+½) and probability density for each quantum state. Zero-point energy ½ℏω cannot be removed — it is a quantum uncertainty effect; the lowest phonon energy in a crystal lattice is 7.6 meV for GaAs (ω ≈ 37 meV acoustic phonon).
Inputs
N
Count of items or occurrences.
Omega Rad S
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Results
energy E_n (eV)
Sample size or count used in the calculation.
energy E_n (meV)
Sample size or count used in the calculation.
zero-point energy E₀ (eV)
Sample size or count used in the calculation.
E_n = ℏω(n + 1/2)
Sample size or count used in the calculation.
energy above ZPE
Sample size or count used in the calculation.
classical turning points
The classification assigned based on the computed value.