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--- wave_packets [2021/02/17 18:46] – [1.ix.3 Motion of Wave Packets] admin
+++ wave_packets [2021/02/18 00:24] (current) – [In Class Activities] admin
@@ Line 163: / Line 163: @@
     - $m=9.11\times 10^{-31}\,\text{kg}$ (the mass of an electron),
     - $m=70\,\text{kg}$ (the mass of a physics instructor).
-====== In Class Activities ======
-  - Use
-  \begin{align*}v_p & = \frac{\omega}{k},& v_g & = \frac{\mathrm{d}\omega}{\mathrm{d}k}, \end{align*}
-  together with
-  \begin{align*}E & = \hbar \omega, & p & = \hbar k, \end{align*}
-  to show that
-  \begin{align*}v_p & = \frac{E}{p}, & v_g & = \frac{\mathrm{d}E}{\mathrm{d}p}.\end{align*}
-  - Consider a particle with initial position uncertainty $\sigma_0 = 1\,\text{nm}$.  Using
-  \[\sigma_t = \sigma_0\sqrt{1 + \frac{\hbar^2t^2}{4m^2\sigma_0^4}},\]
-  determine how long it would take for the wave packet to have $\sigma_t = 1\,\text{m}$ if
-    - $m = 9.11\times 10^{-31}\,\text{kg}$ (the mass of an electron),
-    - $m = 70\,\text{kg}$ (the mass of a physics instructor).