Teaching Quantum Mechanics with Python

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TEACHING QUANTUM MECHANICS WITH PYTHON Andrew M.C. Dawes @drdawes amcdawes.com https://github.com/amcdawes/QMlabs

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TEACHING _____ WITH PYTHON • Topic-neutral where possible • Some speciﬁc examples • Generalize using other computational frameworks • Jupyter, Python, Github Workﬂow

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• ubiquitous in interactive computing • large community • self-help is built-in (IPython) • notebook self-documenting

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Inline Graphics Markdown GitHub/Gist

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QUTIP • Not a toy - Students start out using a full-power computing framework • Convenient object deﬁnitions • Many existing examples

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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

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Pauli matrix Basis states Density matrix

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POWERFUL SOLVERS • Schrödinger • Master-Equation • Monte-Carlo

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VISUALIZATION TOOLS

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COURSE FORMAT

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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

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TEXTBOOK • Mark Beck, Quantum Mechanics: Theory and Experiment • Matrix-mechanics—an approach to quantum mechanics based on linear algebra aka “Dirac Notation”

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TWO-STATE SYSTEMS • single spin in magnetic ﬁeld • hydrogen atom (ground and excited state) • photon polarization • represented by 2-element vectors

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VECTORS AS STATES Spin-up Spin-down

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VECTORS AS STATES Ground state Excited state

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OPERATOR AS MATRIX Basis change Rotation matrix

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LARGER PROBLEMS • 2x2 is doable by hand • QuTip exposes students to large-scale systems of modern practical relevance

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ROLE OF THE NOTEBOOK

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CHAPTER SPECIFIC • One notebook per chapter • Deﬁnitions and techniques relevant to that content • Solved problems (demo Chap. 4) • Re-created examples (demo Chap. 6)

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“LABS” • Larger (multi-hour) exploration of a topic • Follows chapter content • include chapter problems • in addition to single-photon experiments

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NUMERICAL EXPERIMENTS • Use solvers to explore advanced dynamics • Higher-order problems not tractable by hand • Demo Lab 7

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FINAL THOUGHTS and a call to action

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• “Pythonize” your favorite course textbook • post notebooks or code you develop • be descriptive so we can ﬁnd it TRY IT #foo

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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

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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