As we learned in Example 4.2, in a Gaussian function of the- form  is standard deviation,...

As we learned in Example 4.2, in a Gaussian function of the- form  is standard deviation, or uncertainty, in position. The probability density for a Gaussian wave function would be proportional to squared: ψ(x) squared: Comparing with the time- dependent Gaussian probability of equation (6-35), we see that the uncertainty in position of the time-evolving Gaussian wave function of a free particle is given by

That is, it starts at ε and increases with time. Suppose the wave function of an electron is initially determined to be a Gaussian of 500 nm uncertainty. How' long will it take for the uncertainty in the electron’s position to reach m, the length of a typical automobile?