Interactive simulations and visualizations augment the teaching and learning of quantum mechanics by making equations and concepts come to life. However, graphical visualizations are nearly always limited to a set of hard-coded functionalities. Text-based codes can offer a higher degree of flexibility, but only at the expense of steep learning curves or time investments. We introduce Quantum Composer, which allows the user to build, expand, or explore quantum mechanical simulations by interacting with graphically connectable nodes, each corresponding to a physical concept, mathematical operation, or visualization. Quantum Composer eliminates numerical and programming details while retaining accessibility, emphasis on understanding, and rapid feedback mechanisms. We illustrate its open-ended applicability through a series of examples in introductory and advanced quantum mechanics courses, student projects, and research environments.
REFERENCES
1.
John R.
Hiller
,
Ian D.
Johnston
, and
Ian
Johnson
, Quantum Mechanics Simulations
, 1st ed. (
John Wiley & Sons, Inc
.,
New York
, 1995
).2.
Bernd
Thaller
, Visual Quantum Mechanics: Selected Topics with Computer Generated Animations of Quantum Mechanical Phenomena with Cdrom
, 1st ed. (
Springer-Verlag
,
Berlin
, 2000
).3.
Mario
Belloni
and
Wolfgang
Christian
, “
Physlets for quantum mechanics
,” Comput. Sci. Eng.
5
(1
), 90
–97
(2003
).4.
Dean A.
Zollman
,
N. Sanjay
Rebello
, and
Kirsten
Hogg
, “
Quantum mechanics for everyone: Hands-on activities integrated with technology
,” Am. J. Phys.
70
(3
), 252
–259
(2002
).5.
Lawrence T.
Escalada
,
N.
Sanjay Rebello
, and
Dean A.
Zollman
, “
Student explorations of quantum effects in LEDs and luminescent devices
,” Phys. Teach.
42
(3
), 173
–179
(2004
).6.
Antje
Kohnle
et al, “
Enhancing student learning of two-level quantum systems with interactive simulations
,” Am. J. Phys.
83
(6
), 560
–566
(2015
).7.
Antje
Kohnle
,
Alexander
Jackson
, and
Mark
Paetkau
, “
The difference between a probability and a probability density
,” Phys. Teach.
57
(3
), 190
–192
(2019
).8.
S. B.
McKagan
et al, “
Developing and researching PhET simulations for teaching quantum mechanics
,” Am. J. Phys.
76
(4
), 406
–417
(2008
).9.
Chandralekha
Singh
, “
Interactive learning tutorials on quantum mechanics
,” Am. J. Phys.
76
(4
), 400
–405
(2008
).10.
Antje
Kohnle
et al, “
A new multimedia resource for teaching quantum mechanics concepts
,” Am. J. Phys.
80
(2
), 148
–153
(2012
).11.
C. A.
Weidner
et al, “
Investigating student use of a flexible tool for simulating and visualizing quantum mechanics
” in 2020 PERC Proceedings
(2020
), pp. 563
–568
.12.
S. B.
McKagan
,
K. K.
Perkins
, and
C. E.
Wieman
, “
Deeper look at student learning of quantum mechanics: The case of tunneling
,” Phys. Rev. ST Phys. Educ. Res.
4
(2
), 020103
(2008
).13.
Gina
Passante
and
Antje
Kohnle
, “
Enhancing student visual understanding of the time evolution of quantum systems
,” Phys. Rev. Phys. Ed. Res.
15
, 010110
(2019
).14.
Chandralekha
Singh
, “
Student understanding of quantum mechanics at the beginning of graduate instruction
,” Am. J. Phys.
76
(3
), 277
–287
(2008
).15.
Guangtian
Zhu
and
Chandralekha
Singh
, “
Surveying students' understanding of quantum mechanics in one spatial dimension
,” Am. J. Phys.
80
(3
), 252
–259
(2011
).16.
Emily
Marshman
and
Chandralekha
Singh
, “
Investigating and improving student understanding of the expectation values of observables in quantum mechanics
,” Eur. J. Phys.
38
(4
), 1
–19
(2017
).17.
Emily
Marshman
and
Chandralekha
Singh
, “
Interactive tutorial to improve student understanding of single photon experiments involving a Mach-Zehnder interferometer
,” Eur. J. Phys.
37
(2
), 024001
(2017
).18.
A.
Kohnle
,
C.
Baily
, and
S.
Ruby
, “
Investigating the influence of visualization on student understanding of quantum superposition
,” in 2014 PERC Proceedings
(2014
), pp. 139
–142
.19.
Antje
Kohnle
et al, “
Developing and evaluating animations for teaching quantum mechanics concepts
,” Eur. J. Phys.
31
(6
), 1441
–1455
(2010
).20.
Christof
Keebaugh
,
Emily
Marshman
, and
Chandralekha
Singh
, “
Improving student understanding of fine structure corrections to the energy spectrum of the hydrogen atom
,” Am. J. Phys.
87
(7
), 594
–605
(2019
).21.
Noah S.
Podolefsky
,
Katherine K.
Perkins
, and
Wendy K.
Adams
, “
Computer simulations to classrooms: Tools for change
,” AIP Conf. Proc.
1179
(1
), 233
–236
(2009
).22.
Alexander
Repenning
, “
Moving beyond syntax: Lessons from 20 years of blocks programming in agentsheets
,” J. Visual Languages Sentient Syst.
3
(1
), 68
–91
(2017
).23.
C. J.
Kalkman
, “
LabVIEW: A software system for data acquisition, data analysis, and instrument control
,” J. Clin. Monit.
11
(1
), 51
–58
(1995
).24.
Mitchel
Resnick
et al, “
Scratch: Programming for all
,” J. Commun. ACM
52
(11
), 60
–67
(2009
).25.
J. J.
Sørensen
et al, “
QEngine: A C++ library for quantum optimal control of ultracold atoms
,” Comp. Phys. Commun.
243
, 135
–150
(2019
).26.
Jesper H. M.
Jensen
et al, “
Time-optimal control of collisional
gates in ultracold atomic systems
,” Phys. Rev. A
100
, 052314
(2019
).27.
Jesper H. M.
Jensen
et al, “
Crowdsourcing human common sense for quantum control
,” Phys. Rev. Res.
3
, 013057
(2021
).28.
F.
Dalfovo
et al, “
Theory of Bose-Einstein condensation in trapped gases
,” Rev. Mod. Phys.
71
, 463
–509
(1999
).29.
Wendy
Adams
et al, “
A study of educational simulations Part I - Engagement and learning
,” J. Interactive Learn. Res.
19
(3
), 397
–419
(2008
), <https://www.learntechlib.org/p/24230>.30.
Daniel F.
Styer
, “
Common misconceptions regarding quantum mechanics
,” Am. J. Phys.
64
(1
), 31
–34
(1996
).31.
Chandralekha
Singh
, “
Student understanding of quantum mechanics
,” Am. J. Phys.
69
(8
), 885
–895
(2001
).32.
Rainer
Müller
and
Hartmut
Wiesner
, “
Teaching quantum mechanics on an introductory level
,” Am. J. Phys.
70
(3
), 200
–209
(2002
).33.
E.
Cataloglu
and
R. W.
Robinett
, “
Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career
,” Am. J. Phys.
70
(3
), 238
–251
(2002
).34.
Emily
Marshman
and
Chandralekha
Singh
, “
Framework for understanding the patterns of student difficulties in quantum mechanics
,” Phys. Rev. ST Phys. Educ. Res.
11
, 020117
(2015
).35.
Chandralekha
Singh
and
Emily
Marshman
, “
Review of student difficulties in upper-level quantum mechanics
,” Phys. Rev. ST Phys. Educ. Res.
11
, 020119
(2015
).36.
Wendy
Adams
et al, “
A study of educational simulations Part II - Interface design
,” J. Interactive Learn. Res.
19
(4
), 551
–577
(2008
), <https://www.learntechlib.org/primary/p/24364/>.37.
Nodes are similar to functions in a functional programming paradigm.
38.
J. J.
Sakurai
and
J.
Napolitano
, Modern Quantum Mechanics
, 2nd ed. (
Addison Wesley
,
Reading, MA
, 2011
), pp. 78
–80
.39.
C. J.
Pethick
and
H.
Smith
, Bose-Einstein Condensation in Dilute Gases
(
Cambridge U. P
.,
Cambridge
, 2011
), pp. 159
–162
.40.
Students are given the common REVTeX template in two-column format. The hope is that students feel that their report resembles that of a real research paper.
41.
S.
van Frank
et al, “
Interferometry with non-classical motional states of a Bose-Einstein condensate
,” Nat. Commun.
5
, 4009
–4015
(2014
).42.
O.
Elíasson
et al, “
Spatial tomography of individual atoms in a quantum gas microscope
,” Phys. Rev. A
102
, 053311
(2020
).43.
We often mention to students that they may prefer to use a mouse with Composer, especially those using macOS.
44.
This is described in more detail at <https://www.quatomic.com/composer/reference/faq/>.
45.
For example, to translate from Composer units to units used, e.g., in our quantum gas microscopy experiment, we take m = 1 to correspond to the mass of one Rb-87 atom and the energyscale
to correspond to one photon recoil for a lattice with wavelength 532 nm. For more information, see <https://www.quatomic.com/composer/reference/quantum-composer-basics/units/>.
46.
The rapid oscillations seen in Fig. 9(d) are physical phenomena due to wave function interference arising from multiple reflections at the edges of the anharmonic potential.
47.
“QuSCo: Quantum-enhanced Sensing via Quantum Control,” </http://qusco-itn.eu/>.
48.
R.
Grimm
,
M.
Weidemüller
, and
Y. B.
Ovchinnikov
, “
Optical dipole traps for neutral atoms
,” Adv. At. Mol. Opt. Phys.
42
, 95
–170
(2000
).49.
R. E.
Sapiro
,
R.
Zhang
, and
G.
Raithel
, “
Reversible loss of superfluidity of a Bose-Einstein condensate in a 1D optical lattice
,” New J. Phys.
11
, 013013
(2009
).© 2021 American Association of Physics Teachers.
2021
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
