In discussions of free particle wave packets, authors of quantum mechanics textbooks choose the Gaussian form. Some authors do so without explanation.1 Others state the reason for their choice is that this particular wave packet can be nicely analyzed in closed form.2 Apart from mathematical convenience, why do we choose the Gaussian wave packet? Yes, the Fourier transform of the Gaussian wave function is also Gaussian. Also, the Gaussian wave packet gives rise to the minimum uncertainty product at time t=0. These features are pedagogically useful. But is there something more to the Gaussian wave packet?

In this note, we show that the probability density of any non-Gaussian wave packet becomes approximately Gaussian as it disperses.3 We graphically illustrate this process by considering the example of a rectangular wave packet.

We start with the standard treatment of time dependent wave functions using propagators...

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