More than 35 years ago, French and Taylor1 outlined an approach to teach students and teachers alike how to understand “qualitative plots of bound-state wave functions.” They described five fundamental statements based on the quantum-mechanical concepts of probability and energy (total and potential), which could be used to deduce the shape of energy eigenfunctions. Despite these important and easy-to-follow statements, this approach has not been universally adopted in the teaching of quantum mechanics.2 For example, recent studies have shown that students' conceptual understanding of quantum mechanics on all levels is surprisingly lacking3 and that misconceptions are universal,4 including that of the relationship between the potential energy function and the resulting energy eigenfunction shape. At the same time, the teaching of quantum mechanical concepts in introductory physics has become increasingly important given the modern technological applications that are based on quantum theory (e.g., PET scans and MRIs). However, most treatments of quantum theory on the introductory level are cursory at best, leaving students with the impression that quantum mechanics is little more than abstract mathematics (a belief that remains with students in their future courses).

1.
A. P.
French
and
E. F.
Taylor
, “
Qualitative plots of bound state wave functions
,”
Am. J. Phys.
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(Aug.
1971
).
2.
See, for example,
C.
Singh
,
M.
Belloni
, and
W.
Christian
, “
Improving students' understanding of quantum mechanics
,”
Phys. Today
,
59
,
43
49
(Aug.
2006
).
3.
E.
Cataloglu
and
R.
Robinett
, “
Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career
,”
Am. J. Phys.
70
,
238
251
(March
2002
).
4.
C.
Singh
, “
Student understanding of quantum mechanics
,”
Am. J. Phys.
69
,
885
896
(Aug.
2001
).
5.
W. Christian and M. Belloni, Physlet® Physics: Interactive Illustrations, Explorations, and Problems for Introductory Physics (Prentice Hall, Upper Saddle River, NJ, 2004).
6.
M. Belloni, W. Christian, and A. J. Cox, Physlet® Quantum Physics: An Interactive Introduction (Prentice Hall, Upper Saddle River, NJ, 2006).
7.
C. G.
Hood
, “
Teaching about quantum theory
,”
Phys. Teach.
31
,
290
293
(May
1993
);
A.
Hobson
, “
Teaching quantum theory in the introductory course
,”
Phys. Teach.
34
,
202
210
(April
1996
);
M.
Normandeau
, “
Putting the humanity back into quantum physics
,”
Phys. Teach.
43
,
524
526
(Nov.
2005
).
8.
M. C.
Wittmann
,
J. T.
Morgan
, and
L.
Bao
, “
Addressing student models of energy loss in quantum tunneling
,”
Eur. J. Phys.
26
,
939
950
(Nov.
2005
).
9.
R.
Müller
and
H.
Wiesner
, “
Teaching quantum mechanics on the introductory level
,”
Am. J. Phys.
70
,
200
209
(March
2002
).
10.
R. M.
Kolbas
and
N.
Holonyak
Jr.
, “
Man-made quantum wells: A new perspective on the finite square-well problem
,”
Am. J. Phys.
52
,
431
437
(May
1984
).
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