Why is a Gaussian function used to represent a wave packet?

[LarryS]

TL;DR

Is there experimental evidence that nature chooses gaussian functions for individual free particle wave packets?

I've read that in standard, one-particle (non-relativistic) Quantum Mechanics, physicists often choose a gaussian function to represent the wave packet (envelope) for a single, free particle. I understand that a gaussian function minimizes both the position and momentum uncertainties. Is there experimental evidence that nature also chooses gaussians for free particles?

Thanks in advance.

 

[anuttarasammyak]

A Gaussian wave packet has the property that its width increases with time while its overall shape is preserved. This behavior is consistent with the idea of a wave packet that remains stable over time. However, since I am not aware of any other wave packets that exhibit similar stability, this cannot be regarded as a proof.

A clear example in which the wavefunction remains exactly Gaussian:
The ground state of the harmonic oscillator is Gaussian. If the Hamiltonian is suddenly set to zero (i.e., the potential is removed and the system becomes a free particle), the wavefunction remains Gaussian and its width increases with time.

 

[renormalize]

TL;DR: Is there experimental evidence that nature chooses gaussian functions for individual free particle wave packets?

Yes, the spreading of single-atom wave packets has been observed experimentally and agrees with theory:
In-situ Imaging of a Single-Atom Wave Packet in Continuous Space