Mathematica

Hands-on Tutorials and Guides by Wolfram

Basics

• Wolfram Screencast: Hands-on start to Mathematica
• Fast Introduction for Math Students

Intermediate

• Calculus and Algebra
• Mathematical Functions
• Function Visualization
• Functions in Complex Plane Visualization
• Data Visualization

Advanced

• Asymptotic Calculus
• Integral Transforms
• Fourier Analysis
• Special Functions for Quantum Mechanics
• Wolfram Quantum Framework

Mathematics for Quantum Physics

• R. Schmied, Using Mathematica for Quantum Mechanics: A Student’s Manual
• Matrix Partial Trace calling via ResourceFunction
• SNEG package for Dirac notation and second quantization calculations

Hands-on Tutorials by the Instructor

• Getting Started

Mathematica Notebooks for Statistical Mechanics

• Black-body radiation: Classical vs. quantum statistical mechanics approach
• Essential quantum concepts using spin examples: Quantum states (vectors or density matrices), operators as observables, probabilities and expectation values
• Sommerfeld expansion
  • B. Cowan, On the chemical potential of ideal Fermi and Bose gases, J. Low Temp. Phys. 197, 412 (2019). | [PDF and Mathematica notebooks]