We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students’ ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students’ understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.

1.
R. R.
Hake
, “
Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses
,”
Am. J. Phys.
66
,
64
74
(
1998
).
2.
Z.
Hrepic
,
D. A.
Zollman
, and
N. S.
Rebello
, “
Comparing students’ and experts’ understanding of the content of a lecture
,”
J. Sci. Educ. Technol.
16
,
213
224
(
2007
).
3.
E.
Schrödinger
, “
An undulatory theory of the mechanics of atoms and molecules
,”
Phys. Rev.
28
,
1049
1070
(
1926
).
4.
E.
Schrödinger
, “
Quantisierung als eigenwertproblem
,”
Ann. Phys. (Paris)
386
,
109
139
(
1926
).
5.
J. J.
Sakurai
,
Modern Quantum Mechanics
(
Addison-Wesley
,
Reading
,
1994
).
6.
L. D.
Landau
and
L. M.
Lifshitz
,
Quantum Mechanics
(
Elsevier
,
Oxford
,
1977
), 3rd ed.
7.
H.
Everett
, “
Relative state formulation of quantum mechanics
,”
Rev. Mod. Phys.
29
,
454
462
(
1957
).
8.
J. A.
Wheeler
, “
Assessment of Everett’s ‘relative state’ formulation of quantum theory
,”
Rev. Mod. Phys.
29
,
463
465
(
1957
).
9.
R. P.
Feynman
,
Quantum Electrodynamics
(
Westview Press
,
Princeton
,
1998
).
10.
J.
Bardeen
,
L. N.
Cooper
, and
J. R.
Schrieffer
, “
Theory of superconductivity
,”
Phys. Rev.
108
,
1175
1204
(
1957
).
11.
J. S.
Bell
, “
On the Einstein-Podolsky-Rosen paradox
,”
Physics (Long Island City, N.Y.)
1
,
195
200
(
1964
).
12.
D.
Bohm
,
The Undivided Universe
(
Routledge
,
New York
,
1998
).
13.
A.
Aspect
,
P.
Grangier
, and
G.
Roger
, “
Experimental test of realistic local theories via Bell’s theorem
,”
Phys. Rev. Lett.
47
,
460
463
(
1981
).
14.
A.
Aspect
,
J.
Dalibard
, and
G.
Roger
, “
Experimental test of Bell’s inequalities using time-varying analyzers
,”
Phys. Rev. Lett.
49
,
1804
1807
(
1982
).
15.
M. E.
Peskin
and
D. V.
Schroeder
,
An Introduction to Quantum Field Theory
(
Westview
,
New York
,
1995
).
16.
C.
Singh
, “
Student understanding of quantum mechanics at the beginning of graduate instruction
,”
Am. J. Phys.
76
,
277
287
(
2008
).
17.
L. C.
McDermott
and
E. F.
Redish
, “
Resource letter on physics education research
,”
Am. J. Phys.
67
,
755
767
(
1999
).
18.
B. S.
Ambrose
, “
Investigation of student understanding of the wave-like properties of light and matter
,” in
2004 Physics Education Research Conference Proceedings
, edited by
J.
Marx
,
P.
Heron
, and
S.
Franklin
(
AIP Press
,
Melville, NY
,
2005
).
19.
M. C.
Wittmann
,
R. N.
Steinberg
,
E. F.
Redish
, and
the University of Maryland Physics Education Research Group
,
Activity-Based Tutorials
(
Wiley
,
New York
,
2005
), Vol.
2
.
20.
M. C.
Wittmann
, “
Lab-tutorials für den quantenphysik unterricht
,”
Prax. Naturwiss., Phys. Sch.
55
,
16
21
(
2006
).
21.
S. B.
McKagan
,
K. K.
Perkins
, and
C. E.
Wieman
, “
Reforming a large lecture modern physics course for engineering majors using a PER-based design
,” in
2006 Physics Education Research Conference Proceedings
, edited by
L.
McCullough
,
P.
Heron
, and
L.
Hsu
(
AIP Press
,
Melville, NY
,
2007
).
22.
S. B.
McKagan
,
K. K.
Perkins
,
M.
Dubson
,
C.
Malley
,
S.
Reid
,
R.
LeMaster
, and
C. E.
Wieman
, “
Developing and researching PhET simulations for teaching quantum mechanics
,”
Am. J. Phys.
76
,
406
417
(
2008
).
23.
S. B.
McKagan
,
W.
Handley
,
K. K.
Perkins
, and
C. E.
Wieman
, “
A research-based curriculum for teaching the photoelectric effect
,”
Am. J. Phys.
77
,
87
94
(
2009
).
24.
C.
Singh
, “
Interactive learning tutorials on quantum mechanics
,”
Am. J. Phys.
76
,
400
405
(
2008
).
25.
B. R.
Patton
, “
Group learning-based approach to the graduate electrodynamics course: Jackson by inquiry
,”
APS Forum on Education Newsletter
, ⟨www.aps.org/units/fed/newsletters/aug96/⟩.
26.
B. R.
Patton
, “
A simple model for why an active learning approach works best: Experiences with a “Jackson by inquiry” electromagnetism course
,”
2007 APS March Meeting
, ⟨meetings.aps.org/link/BAPS.2007. MAR.J5.3⟩.
27.
L. I.
Schiff
,
Quantum Mechanics
(
McGraw-Hill
,
New York
,
1968
), 3rd ed.
28.
A.
Peres
,
Quantum Theory: Concepts and Methods
(
Kluwer Academic
,
Norwell, MA
,
1995
).
29.
C.
Cohen-Tannoudji
,
B.
Diu
, and
F.
Laloë
,
Quantum Mechanics
(
Wiley
,
New York
,
1977
).
30.
A. F. J.
Levi
,
Applied Quantum Mechanics
(
Cambridge U. P.
,
New York
,
2006
), 2nd ed.
31.
J.-L.
Basdevant
and
J.
Dalibard
,
Quantum Mechanics
(
Springer
,
New York
,
2005
), corr. 2nd printing ed.
32.
A. I. M.
Rae
,
Quantum Mechanics
(
Taylor and Francis
,
New York
,
2002
), 4th ed.
33.
K.
Gottfried
and
T.-M.
Yan
,
Quantum Mechanics
(
Springer
,
New York
,
2004
), 2nd ed.
34.
M.
Le Bellac
,
Quantum Physics
(
Cambridge U. P.
,
New York
,
2006
).
35.
W.
Gerlach
and
O.
Stern
, “
Der experimentelle nachweis der richtungsquantelung im magnetfeld
,”
Z. für Phys. A
9
,
349
352
(
1922
).
36.
R. N.
Steinberg
,
G. E.
Oberem
, and
L. C.
McDermott
, “
Development of a computer-based tutorial on the photoelectric effect
,”
Am. J. Phys.
64
,
1370
1379
(
1996
).
37.
M. C.
Wittmann
,
R. N.
Steinberg
, and
E. F.
Redish
, “
Investigating student understanding of quantum physics: Spontaneous models of conductivity
,”
Am. J. Phys.
70
,
218
226
(
2002
).
38.
M. C.
Wittmann
,
J. T.
Morgan
, and
L.
Bao
, “
Addressing student models of energy loss in quantum tunneling
,”
Eur. J. Phys.
26
,
939
950
(
2005
).
39.
S. B.
McKagan
and
C. E.
Wieman
, “
Exploring student understanding of energy through the Quantum Mechanics Conceptual Survey
,” in
2005 Physics Education Research Conference Proceedings
, edited by
P.
Heron
,
L.
McCullough
, and
J.
Marx
(
AIP Press
,
Melville, NY
,
2006
).
40.
I. D.
Johnston
,
K.
Crawford
, and
P. R.
Fletcher
, “
Student difficulties in learning quantum mechanics
,”
Int. J. Sci. Educ.
20
,
427
446
(
1998
).
41.
C.
Singh
, “
Student understanding of quantum mechanics
,”
Am. J. Phys.
69
,
885
895
(
2001
).
42.
H.
Sadaghiani
and
L.
Bao
, “
Student difficulties in understanding probability in quantum mechanics
,” in
2005 Physics Education Research Conference Proceedings
, edited by
P.
Heron
,
L.
McCullough
, and
J.
Marx
(
AIP Press
,
Melville, NY
,
2006
).
43.
D. T.
Brookes
and
E.
Etkina
, “
Do our words really matter? Case studies from quantum mechanics
,” in
2005 Physics Education Research Conference Proceedings
, edited by
P.
Heron
,
L.
McCullough
, and
J.
Marx
(
AIP Press
,
Melville, NY
,
2006
).
44.
P.
Heller
,
R.
Keith
, and
S.
Anderson
, “
Teaching problem solving through cooperative grouping. Part 1: Group versus individual problem solving
,”
Am. J. Phys.
60
,
627
636
(
1992
).
45.
E.
Mazur
,
Peer Instruction: A User’s Manual
(
Prentice Hall
,
Upper Saddle River, NJ
,
1997
).
46.
M. B.
Rowe
, “
Wait time: Slowing down may be a way of speeding up!
,”
J. Teacher Educ.
37
,
43
50
(
1986
).
48.
S. B.
McKagan
,
K. K.
Perkins
, and
C. E.
Wieman
, “
The design and validation of the Quantum Mechanics Conceptual Survey
” (in preparation).
49.
S. J.
Pollock
, “
A Longitudinal Study of the Impact of Curriculum on Conceptual Understanding in E&M
,” in
2007 Physics Education Research Conference Proceedings
, edited by
L.
Hsu
,
C.
Henderson
, and
L.
McCullough
(
AIP Press
,
Melville, NY
,
2007
).
50.
K. K.
Perkins
,
W. K.
Adams
,
N. D.
Finkelstein
,
S. J.
Pollock
, and
C. E.
Wieman
, “
Correlating student attitudes with student learning using the Colorado Learning Attitudes about Science Survey
,” in
2004 Physics Education Research Conference Proceedings
, edited by
J.
Marx
,
P.
Heron
, and
S.
Franklin
(
AIP Press
,
Melville, NY
,
2005
).
51.
K. K.
Perkins
,
M. M.
Gratny
,
W. K.
Adams
,
N. D.
Finkelstein
, and
C. E.
Wieman
, “
Towards characterizing the relationship between students’ self-reported interest in and their surveyed beliefs about physics
,” in
2005 Physics Education Research Conference Proceedings
, edited by
P.
Heron
,
L.
McCullough
, and
J.
Marx
(
AIP Press
,
Melville, NY
,
2006
).
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.