## Advanced Quantum Mechanics III

Here you will learn how to treat complex quantum systems with perturbation theory and how to describe many-body quantum systems with second quantization.

Both your table and your coffee cup are (usually) in a solid state. Solid state physics studies all properties of solids, such as thermal and electrical conductivity, its atomic structure and other physical quantities.

Here you will learn how to treat complex quantum systems with perturbation theory and how to describe many-body quantum systems with second quantization.

` $$ m \, \class{violet}{\lambda} ~=~ 2\class{blue}{d} \, \sin(\class{gray}{\theta}) $$ `

Learn how to theoretically generate Majorana Zero Modes using the Kitaev chain and how this eliminates quantum errors.

` $$ C_{\text V} ~=~ 9N \, k_{\text B} \left( \frac{T}{T_{\text D}} \right)^3 \int_{0}^{T_{\text D}/T} \frac{u^4 \, \mathrm{e}^u}{(\mathrm{e}^u-1)^2} ~ \text{d}u $$ `

` $$ T_{\text F} ~=~ \frac{\hbar^2}{2m \, k_{\text B}} \, (3\pi^2 \, n)^{2/3} $$ `

` $$ C_{\text V} ~=~ 3N \, k_{\text B} \, \left( \frac{T_{\text E}}{T} \right)^2 \, \frac{ \mathrm{e}^{T_{\text E}/T} }{\left(\mathrm{e}^{T_{\text E}/T} - 1\right)^2} $$ `

Derivation of the Hall voltage (via Hall effect), which depends only on quantities that we can easily determine in an experiment.

` $$ \begin{align}
\omega_{\pm}^2 ~&=~ D \, \left( \frac{1}{m_1} + \frac{1}{m_2} \right) \\\\
~&\pm~ D \, \sqrt{\left(\frac{1}{m_1} + \frac{1}{m_2}\right)^2 ~-~ \frac{4}{m_1 \, m_2}\,\sin^2\left(\frac{k\,a}{2}\right) }
\end{align} $$ `

` $$ \omega(k) ~=~ \sqrt{\frac{4 D}{m} \sin^2\left(\frac{ka}{2}\right)} $$ `