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Commit 616fb034 authored by T. van der Sar's avatar T. van der Sar
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Update 2_debye_model.md

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### Quick warm-up exercises
1. Express the heat capacity for low $T$ in terms of $T_D$.
2. Make a sketch of the heat capacity in the low $T$ for two different Debye temperatures.
1. Express the heat capacity in the low-$T$ limit in terms of $T_D$.
2. Make a sketch of the heat capacity in the low-$T$ limit for two different Debye temperatures.
3. Why are there only 3 polarizations when there are 6 degrees of freedom in three-dimensions for an oscillator?
4. Convert the two-dimensional integral $\int\mathrm{d}k_x\mathrm{d}k_y$ to a one-dimensional integral.
5. The Einstein model has the eigenfrequency $\omega_0 = k_\mathrm{B} T_E/\hbar$ of the quantum harmonic oscillators modeling the atoms as a material-dependent free fitting parameter. What is the material-dependent parameter that plays a similar role in the Debye model?
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