Equipartition theorem

Temperature T

Stiffness a

Enable quantization

Level spacing Δ = ℏω

Fit upper plots to current values Axes stay fixed as you move the sliders.

Position density and potential

━━ p(x), left   ━━ U(x) = ax², right

Contributions to mean potential energy

Energy above the ground state versus temperature

━━ ⟨U⟩ − U₀   ━━ ⟨H⟩ − E₀   ╌╌ classical T/2 and T

Points mark the selected temperature. Ground-state energy is subtracted here; both curves tend to zero as T → 0.