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Using Mathematica for Quantum Mechanics

A Student’s Manual

  • Book
  • © 2020

Overview

Authors:
  1. Roman Schmied

    1. Department of Physics, University of Basel, Basel, Switzerland

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  • Demonstrates how complex problems in quantum mechanics can be solved using computational tools

  • Includes practical exercises after each chapter, promoting an active understanding of the subject

  • Bridges the gap between simple analytic calculations and large-scale computations for molecular structures, crystalline solids, and lattice models

  • Written for students with no prior background in the programming language Mathematica

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Wolfram Language Overview

    • Roman Schmied
    Pages 1-31

  3. Quantum Mechanics: States and Operators

    • Roman Schmied
    Pages 33-50

  4. Spin and Angular Momentum

    • Roman Schmied
    Pages 51-90

  5. Quantum Motion in Real Space

    • Roman Schmied
    Pages 91-136

  6. Combining Spatial Motion and Spin

    • Roman Schmied
    Pages 137-152

  7. Back Matter

    Pages 153-193
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Keywords

About this book

This book revisits many of the problems encountered in introductory quantum mechanics, focusing on computer implementations for finding and visualizing analytical and numerical solutions. It subsequently uses these implementations as building blocks to solve more complex problems, such as coherent laser-driven dynamics in the Rubidium hyperfine structure or the Rashba interaction of an electron moving in 2D. The simulations are highlighted using the programming language Mathematica. No prior knowledge of Mathematica is needed; alternatives, such as Matlab, Python, or Maple, can also be used.

Authors and Affiliations

  • Department of Physics, University of Basel, Basel, Switzerland

    Roman Schmied

About the author

PD Dr. Roman Schmied studied physics at the École Polytechnique Fédérale de Lausanne and the University of Texas at Austin. He wrote his diploma thesis on helium nanodroplet spectroscopy at Princeton University with Kevin Lehmann and Giacinto Scoles, and later obtained his Ph.D. from the same group, working on the superfluidity of helium nanodroplets and on the spectroscopy of molecules solvated within these droplets. He carried out his postdoctoral work at the Max Planck Institute of Quantum Optics in Garching, Germany, where he first began working with quantum simulators and quantum simulations. After a short stay at the NIST ion storage group in Boulder, USA, he took on his current position at the University of Basel, where he was habilitated in 2017. Since 2016 he has also been working at the University’s Human Optics Lab, where he is currently using digital technology for child health, particularly eye health.

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