Teaching Quantum Mechanics with Python

Talk from PyCon 2017 Education Summit. A presentation on the use of QuTip and Jupyter Notebooks in an upper-division physics class on Quantum Mechanics.

Transcript

1. TEACHING QUANTUM MECHANICS WITH PYTHON Andrew M.C. Dawes @drdawes amcdawes.com https://github.com/amcdawes/QMlabs
2. TEACHING _____ WITH PYTHON • Topic-neutral where possible • Some specific examples • Generalize using other computational frameworks • Jupyter, Python, Github Workflow
4. • ubiquitous in interactive computing • large community • self-help is built-in (IPython) • notebook self-documenting
6. Inline Graphics Markdown GitHub/Gist
8. QUTIP • Not a toy - Students start out using a full-power computing framework • Convenient object definitions • Many existing examples
9. STANDARD OBJECTS • Analogous to: from numpy import pi from scipy.constants import speed_of_light • QuTip defines standard quantum objects • objects in the programming sense, not the physical sense • The same objects we see in the textbook
10. Pauli matrix Basis states Density matrix
11. POWERFUL SOLVERS • Schrödinger • Master-Equation • Monte-Carlo
12. VISUALIZATION TOOLS
13. COURSE FORMAT
14. AUDIENCE • Junior/Senior Physics Majors • No CS experience req’d • 50% had intro-level C++ • 14-18 students • 3x 65-min & a 3-hr lab
15. TEXTBOOK • Mark Beck, Quantum Mechanics: Theory and Experiment • Matrix-mechanics—an approach to quantum mechanics based on linear algebra aka “Dirac Notation”
16. TWO-STATE SYSTEMS • single spin in magnetic field • hydrogen atom (ground and excited state) • photon polarization • represented by 2-element vectors
17. VECTORS AS STATES Spin-up Spin-down
18. VECTORS AS STATES Ground state Excited state
19. OPERATOR AS MATRIX Basis change Rotation matrix
20. LARGER PROBLEMS • 2x2 is doable by hand • QuTip exposes students to large-scale systems of modern practical relevance
21. ROLE OF THE NOTEBOOK
22. CHAPTER SPECIFIC • One notebook per chapter • Definitions and techniques relevant to that content • Solved problems (demo Chap. 4) • Re-created examples (demo Chap. 6)
23. “LABS” • Larger (multi-hour) exploration of a topic • Follows chapter content • include chapter problems • in addition to single-photon experiments
25. NUMERICAL EXPERIMENTS • Use solvers to explore advanced dynamics • Higher-order problems not tractable by hand • Demo Lab 7
26. FINAL THOUGHTS and a call to action
27. • “Pythonize” your favorite course textbook • post notebooks or code you develop • be descriptive so we can find it TRY IT #foo
28. KEY POINTS • Use real-world frameworks • Re-create examples to reinforce what students see in other references • Don’t be afraid to give fully-worked examples • Encourage tinkering
29. THANK YOU • PyCon logo and banner were designed by Beatrix Bodó • Pacific Univ., Murdock Trust, RCSA, NSF logos used with permission • Jupyter & QuTip open source projects • Lab photos Courtesy of M. Beck @ Whitman College • Images and logo from QuTip documentation, QuTip is: J. R. Johansson, P. D. Nation, and F. Nori: "QuTiP 2: A Python framework for the dynamics of open quantum systems.", Comp. Phys. Comm. 184, 1234 (2013) [DOI: 10.1016/j.cpc.2012.11.019]. Credits: Andrew M.C. Dawes @drdawes amcdawes.com https://github.com/amcdawes/QMlabs