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Poster has been reminded to always show effort in schoolwork thread starts

- Homework Statement
- See attached images.

- Relevant Equations
- ##\omega=2\pi f, k=\frac{2 \pi}{\lambda}, E=\hbar \omega, p=\hbar k##

Show that ##v_{av}=\frac{\hbar k_2 + \hbar k_1}{2m}## is equal to ##v_{av}=\frac{\omega_2 - \omega_1}{k_2-k_1}##. Which of the identities listed above (if any) would make the sign change between ##k_2## and ##k_1##?

One can attain a "wave packet" by superposing two or more sinusoidal waves with different wave numbers and amplitudes. How come such a "wave packet" is given by an integral? What area does this integral represent? How come it is not given by, for example, ##\sum_i^n A(k_i) e^{i(k_ix-\omega t)} ## (or by the formula for the Fourier series?)

One can attain a "wave packet" by superposing two or more sinusoidal waves with different wave numbers and amplitudes. How come such a "wave packet" is given by an integral? What area does this integral represent? How come it is not given by, for example, ##\sum_i^n A(k_i) e^{i(k_ix-\omega t)} ## (or by the formula for the Fourier series?)

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