ubuntu2404
\contentsline {section}{\numberline {1}Introduction to Computational Physics in LaTeX}{3}{section.1}%
\contentsline {section}{\numberline {2}Quantum Mechanics Simulations}{3}{section.2}%
\contentsline {subsection}{\numberline {2.1}Time-Dependent Schrödinger Equation Solver}{3}{subsection.2.1}%
\contentsline {subsection}{\numberline {2.2}Quantum Harmonic Oscillator Eigenstates}{4}{subsection.2.2}%
\contentsline {subsection}{\numberline {2.3}Particle in a Box: Quantum Confinement Effects}{5}{subsection.2.3}%
\contentsline {section}{\numberline {3}Statistical Mechanics and Monte Carlo Simulations}{6}{section.3}%
\contentsline {subsection}{\numberline {3.1}Ising Model Monte Carlo Simulation}{6}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Partition Function and Thermodynamic Properties}{7}{subsection.3.2}%
\contentsline {section}{\numberline {4}Condensed Matter Physics Applications}{8}{section.4}%
\contentsline {subsection}{\numberline {4.1}Electronic Band Structure Calculations}{8}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Fermi Surface and Electronic Properties}{9}{subsection.4.2}%
\contentsline {subsection}{\numberline {4.3}Phonon Dispersion Relations}{10}{subsection.4.3}%
\contentsline {section}{\numberline {5}Advanced Topics and Applications}{11}{section.5}%
\contentsline {subsection}{\numberline {5.1}Quantum Many-Body Systems}{11}{subsection.5.1}%
\contentsline {section}{\numberline {6}Computational Techniques and Best Practices}{13}{section.6}%
\contentsline {subsection}{\numberline {6.1}Numerical Precision and Error Analysis}{13}{subsection.6.1}%
\contentsline {section}{\numberline {7}Conclusion and Future Directions}{13}{section.7}%
\contentsline {subsection}{\numberline {7.1}Computational Resources and Performance}{14}{subsection.7.1}%
\contentsline {subsection}{\numberline {7.2}Extensions and Applications}{14}{subsection.7.2}%
\contentsline {section}{\numberline {A}Code Repository and Data}{15}{appendix.A}%
\contentsline {section}{\numberline {B}Compilation Instructions}{15}{appendix.B}%