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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| module_1_summary [2021/03/01 18:34] – [Wave Packets] admin | module_1_summary [2021/03/01 18:35] (current) – [Phase and Group Velocity] admin | ||
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| When there is dispersion, wave packets spread in time. For a Gaussian wave packet with initial position uncertainty $\sigma_0$, the uncertainty at time $t$ grows to | When there is dispersion, wave packets spread in time. For a Gaussian wave packet with initial position uncertainty $\sigma_0$, the uncertainty at time $t$ grows to | ||
| \[\sigma_t = \sigma_0 \sqrt{1 + \frac{\hbar^2 t^2}{4m^2\sigma_0^4}}.\] | \[\sigma_t = \sigma_0 \sqrt{1 + \frac{\hbar^2 t^2}{4m^2\sigma_0^4}}.\] | ||
| - | ===== Phase and Group Velocity ===== | ||
| - | ===== Spreading of Wave Packets ===== | + | |