Quantum Harmonic Oscillator Calculator
Calculate energy levels and wave functions for the quantum harmonic oscillator
Quantum Results
Energy Level E_n
5.2729e-20 J
3.2914e-1 eV
Zero-Point Energy
5.2729e-20 J
Characteristic Length
3.4025e-10 m
Wave Function ψ(x)
4.0720e+4
Probability Density |ψ|²
1.6581e+9
Spring Constant k
9.1090e-1 N/m
Classical Comparison
Classical Amplitude
3.4025e-10 m
Classical Frequency
1.5915e+14 Hz
Classical Period
6.2832e-15 s
About the Quantum Harmonic Oscillator
The quantum harmonic oscillator has equally spaced energy levels: E_n = ℏω(n + 1/2). Even in the ground state (n=0), the oscillator has non-zero energy (zero-point energy). The wave functions are Gaussian functions multiplied by Hermite polynomials.
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: University Physics
by Young & Freedman