CourseLevel 4 (up to Physics M.Sc.)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.
FormulaBragg's Law (Diffraction Order, Wavelength, Lattice Constant, Angle) $$ m \, \class{violet}{\lambda} ~=~ 2\class{blue}{d} \, \sin(\class{gray}{\theta}) $$
LessonLevel 4 (up to Physics M.Sc.)Kitaev's Chain: How to Get Unpaired Majorana Fermions Learn how to theoretically generate Majorana Zero Modes using the Kitaev chain and how this eliminates quantum errors.
FormulaThermal Capacity (Debye Approximation) $$ C_{\text V} ~=~ 9N \, k_{\text B} \left( \frac{T}{T_{\text D}} \right)^3 \int_{0}^{T_{\text D}/T} \frac{u^4 \, \mathrm{e}^u}{(\mathrm{e}^u-1)^2} ~ \text{d}u $$
FormulaFree Electron Gas in 3d (Fermi Temperature) $$ T_{\text F} ~=~ \frac{\hbar^2}{2m \, k_{\text B}} \, (3\pi^2 \, n)^{2/3} $$
FormulaThermal Capacity (Einstein Approximation) $$ C_{\text V} ~=~ 3N \, k_{\text B} \, \left( \frac{T_{\text E}}{T} \right)^2 \, \frac{ \mathrm{e}^{T_{\text E}/T} }{\left(\mathrm{e}^{T_{\text E}/T} - 1\right)^2} $$
Derivation Level 3 (up to Physics B.Sc.)Hall Voltage due to the Hall Effect Derivation of the Hall voltage (via Hall effect), which depends only on quantities that we can easily determine in an experiment.
FormulaDispersion Relation (Crystal with Diatomic Basis) $$ \begin{align} \omega_{\pm}^2 ~&=~ D \, \left( \frac{1}{m_1} + \frac{1}{m_2} \right) \\\\ ~&\pm~ D \, \sqrt{\left(\frac{1}{m_1} + \frac{1}{m_2}\right)^2 ~-~ \frac{4}{m_1 \, m_2}\,\sin^2\left(\frac{k\,a}{2}\right) } \end{align} $$
FormulaDispersion Relation (Crystal with Monatomic Basis) $$ \omega(k) ~=~ \sqrt{\frac{4 D}{m} \sin^2\left(\frac{ka}{2}\right)} $$
LessonLevel 3 (up to Physics B.Sc.)Photolithography: How to Make a Circuit in 7 Easy Steps Here you will learn how integrated circuits in semiconductor technology are manufactured step by step using lithography technique.
