Normalization of the Gaussian for Wavefunctions

Small White Board Question: Normalization of the Gaussian for Wavefunctions

Periodic Systems 2022

Students find a wavefunction that corresponds to a Gaussian probability density.

Small White Board Question schedule 5 min. description Student handout (PDF)

This ingredient is used in the following sequences
1. << Fourier Transform of a Gaussian | Fourier Transforms and Wave Packets |

The Gaussian \begin{equation} {\cal P}(x)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation} is normalized so that the area under the curve is equal to one. If this Gaussian represents the probability density for a free quantum mechanical particle, what is a possible wavefunction?

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