Harmonic Oscillator

The harmonic potential has equally spaced levels. It is often used as an approximation to the vibrational potential between two atoms in a diatomic or the movements of the nuclei in a polyatomic molecule. For the first and second levels - those most important for thermodynamic calculations - this is a fair approximation, see the anharmonic, real potential "5".

Make sure to observe the first level being only 1/2 levelspace above the minimum of the potential. This represents the zero-point energy (meaning the vibrational energy existing even at zero Kelvin) of the oscillator as requested by Heisenberg's Uncertainty Relations. The minimum of the potential is not accessible to the oscillator. Realize, that this result is produced here without any direct reference to Heisenberg's principle, just by numerically solving Schrödinger's wave equation, see program listing for comments.