The ground state energy of classical oscillator is zero, while that of quantum oscillators has finite (zero-point) energy. How can you demonstrate that (not by calculations but by some experiments or observations)

In the correct explanation of quantum mechanics there is a minimum energy, so the electrons must rotate around the nuclei and the atoms are stable.

Explanation:

If matter behaved like a classical oscillator when its temperature drops, its energy should decrease, therefore at the temperature of absolute zero there would be no energy, so the electrons should not rotate around the nuclei, which is incompatible with the reality.

In the correct explanation of quantum mechanics there is a minimum energy, so the electrons must rotate around the nuclei and the atoms are stable.

This is observed in experiments where the light emitted by atoms is measured, which at low temperatures has a deferent minimum value of zero.