Schrödinger equation in 1D
t = 0.0e+0 T₀States in superposition · 1
0
1
2
3
4
5
6
7
Click to toggle a state; double-click, right-click or Shift-click to show only that state. The filled sector is the state's phase.
Harmonic Oscillator
The quantum harmonic oscillator models a particle in a parabolic potential well, like a mass on a spring. It is the most important quantum system in chemistry because the bottom of almost any bound potential is locally parabolic, so it describes small-amplitude vibrations of molecules in their equilibrium geometry.
Energy levels are evenly spaced: . The wavefunctions are Hermite polynomials multiplied by a Gaussian envelope, so they decay smoothly into the classically-forbidden region beyond the turning points.