Course Introduction to Solid State Physics
Structure, transport and interaction in solid matter
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
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Related formulas
Formula $$ D(W) ~=~ \frac{V}{2\pi^2} \, \left(\frac{2\class{brown}{m}}{\hbar^2}\right)^{3/2} \, \sqrt{W} $$Free electron gas in 3d (density of states)
Formula $$ D ~=~ \frac{A}{\pi} \, \frac{2\class{brown}{m}}{\hbar^2} $$Free electron gas in 2d (density of states)
Formula $$ D(W) ~=~ \frac{L}{\pi} \, \left(\frac{2\class{brown}{m}}{\hbar^2}\right)^{1/2} \, \frac{1}{\sqrt{W}} $$Free electron gas in 1d (density of states)
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Related formulas
Formula $$ \omega(k) ~=~ \sqrt{\frac{4 D}{\class{brown}{m}} \sin^2\left(\frac{ka}{2}\right)} $$Dispersion Relation (Crystal with Monatomic Basis)
Formula $$ v_{\text g} ~=~ \sqrt{\frac{D \, a^2}{\class{brown}{m}}} \, \cos\left(\frac{1}{2} \, k \, a\right) $$Group Velocity (Oscillation of a Monatomic Chain)
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Questions & Answers
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Formula $$ \begin{align} \omega_{\pm}^2 ~&=~ D \, \left( \frac{1}{m_1} + \frac{1}{m_2} \right) \\\\ ~&\pm~ D \, \sqrt{\left(\frac{1}{m_1} + \frac{1}{m_2}\right)^2 ~-~ \frac{4}{m_1 \, m_2}\,\sin^2\left(\frac{k\,a}{2}\right) } \end{align} $$Dispersion Relation (Crystal with Diatomic Basis)
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Questions & Answers
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