CHAPTER 2
QUANTUM MECHANICS LITERATURE REVIEW
2.1 INTRODUCTION
It has already been noted that there has not been much education research
devoted to the teaching of quantum mechanics. The subject is far too specialised to
have much presence in mainstream education literature. What work has been done
is reported mainly in Chemistry and Physics journals.
The following literature summary covers a broad selection of articles which
were intended by their authors to be used by educators of the subject. Chemistry
and physics articles have been treated separately to reflect the differences in the
types and styles of articles, within each discipline area the articles have been
classified and grouped under one of the following four headings – History;
Teaching specific ideas and concepts; Course materials; or Education research.
For a comprehensive categorised literature bibliography covering quantum
mechanics please refer to Appendix 8 for a Quantum Chemistry Literature Survey
and Appendix 9 for a Quantum Physics Literature Survey.
2.2 CHEMISTRY RELATED
Chemistry education research has had a presence since the 1920’s with the
publishing of the Journal of Chemical Education1 in 1924 and provided a broad
forum for all chemical educators. Chemistry education reached a milestone in the
late 1970’s when university chemistry departments recognised and began to
appoint faculty to positions specifically responsible for chemistry education. For
example Purdue University in 1982 established a Division of Chemical Education 2
and offers higher degree programs in chemical education.
In relation to the teaching of quantum mechanics, the period 1970 through
to the commencement of this research has seen a steady number of articles in
Journal of Chemical Education – refer to http://jchemed.chem.wisc.edu/index.html
Completing the Program with a Division of Chemical Education
by G.M. Bodner and J. Dudley Herron – refer to
http://chemed.chem.purdue.edu/chemed/bodnergroup/archive/publications/completing.
html
1
2
11
12
chemical education literature devoted to quantum theory and introductory
quantum mechanics.
These include short essays addressing historical and
philosophical issues, descriptions of atomic models and bonding, representations of
bonding and energy levels, example problems suitable for presentation and
computer simulations.
In Appendix 8 Quantum Chemistry Literature Survey, the papers have been
categorised and grouped into the following structure.
HISTORY
Quantum Chemistry – History
TEACHING OF IDEAS AND CONCEPTS
Quantum Chemistry - Teaching Concepts
Interpretations
Bonding & Structure
Atoms
Orbitals
Mathematics
Specific
Quantum Chemistry - Lecture Demonstrations & Laboratory
Demonstrations
Laboratory
Quantum Chemistry - Computational Ideas
Curriculum Changes & Delivery
Software Programs
Wave Function Software
Atomic Structure & Orbital Programs
Web
EDUCATION RESEARCH
Quantum Chemistry - Education Research
2.2.1 Chemistry – History & Teaching of Ideas and Concepts Papers
Though these papers cover a wide variety of topics, their approach is
surprisingly similar. By and large they focus mainly on providing teaching support
materials.
One paper, chosen more or less at random, can be taken to be
representative and contain the common elements addressed. It is entitled Presenting
the Bohr Atom (Haendlers, 1982) and is typical of the format of the majority of this
literature.
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The paper first acknowledges that the current available text material lacks
context and treats the topic in a simplistic way, ignoring the events and debates that
lead to the formalisation of theories. The paper then describes the context of the
topic, in this case an historical outline of the development of Bohr’s ideas. It cites
and contextualises the observations, theories and experiments from Faraday’s
experiments with electrolysis through to the Schrödinger theory of quantum
mechanics.
The main body of the article then refers back to this preliminary
information. The main topic of this article is entitled ‘Derivation of the Energies of
the Stationary States’ and details the derivation of Bohr’s model. The summary
section entitled ‘The Bohr atom in the Chemistry Curriculum’ then links the ideas
presented in the article back to the undergraduate chemistry curriculum.
The primary inference from this paper, as in other similar articles, is that a
more historically accurate and/or detailed treatment of the material should increase
the student’s understanding of the development of scientific theories. Also it is
proposed that this treatment of the material would also remove some of the
frustration students feel at the arbitrary nature of current textbook presentations.
The themes contained within this grouping of papers does have variation
when compared to the example above, some are less critical of the current material
or methods and focus more on presenting an idea, the utilisation of a tool or simply
offer advice on material delivery in a particular educational setting.
2.2.2 Chemistry – Education Research Papers
The proportion of specifically quantum mechanics education research based
papers is small when compared to the number of aforementioned papers. These
papers predominately address the areas of bonding and atomic structure.
Following is a representative selection of papers.
Patricia Keig and Peter Rubba in their paper Translation of Representations of
the Structure of Matter and its Relationship to Reasoning, Gender, Spatial Reasoning and
Specific Prior Knowledge (Keig, 1993) explore the abilities of students to appropriately
translate between three representations of the structure of matter. The research uses
interviews as the primary research instrument and three variates of paper-andpencil instruments to measure reasoning, spatial reasoning and prior knowledge.
The discussion section of the paper reiterates the research questions and comments
on the findings in terms of translation errors, misunderstandings, misapplications,
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spatial reasoning and gender differences. The conclusion paragraph then relates
the findings to models of knowledge and understanding, then briefly discusses
strategies which may assist instruction to minimise the identified weaknesses.
Georgeios Tsaparlis’s paper entitled Atomic Orbitals, Molecular Orbitals and
Related Concepts (Tsaparlis, 1997) analyses examination scripts of successful
students. The students knowledge and understanding of the following topics was
studied – the definition of an atomic orbital, the real mathematical verses the
complex mathematical forms of the atomic orbitals, the representations (shapes) of
the atomic orbitals, the approximate nature of atomic orbitals for many electron
atoms, Slater determinants, the definition of a molecular orbital, and the nature of
the chemical bond.
The analyses revealed that students did not have a clear
understanding of orbitals, they had difficulty in understanding the conceptual
similarity between the real and complex mathematical forms associated with atomic
orbitals, they confuse the orbital representations, and did not realise the
approximate nature of orbitals for many electron atoms. The paper then discusses
the implications of these finding for instruction and the curriculum, followed by
instructional strategies and suggestions for secondary and general chemistry
curricula.
The chemical education research papers related to quantum mechanics have
adopted well tested educational tools which are commonly utilised in mainstream
science education research. The research formats are narrow and tend to focus on
exploring the understanding of a specific concept(s), addressing the difficulties
and/or misconceptions students’ hold, followed by a discussion concerning the
implications to instruction and curricula.
2.2.3 Chemistry – Papers
In summary, the majority of chemical education publications relating to
quantum mechanics, provide useful teaching materials such as historical reviews
and presentation analogies. They generally conclude that these materials would
enhance a student’s understanding of the quantum concepts, but do not make
reference to supporting education research. There is therefore little emphasis on
pedagogy.
This lack of pedagogical research into the deeper question of learning is
most probably due to the fact that quantum mechanics is not currently considered a
15
particularly important area for the chemical education research community. This
would no doubt be related to the sheer number of topics that have to be covered,
and quantum mechanics is perceived to be only a very small part of the
undergraduate chemistry curricula.
2.3 PHYSICS RELATED
Physics education research has been growing over the past 25 years. For a
comprehensive literature reading list refer to the University of Marylands, Research
in Physics Education (RIPE) WEB site (URL http://www.umd.edu/ripe). At the
American Association of Physics Teachers (AAPT) held in 1996, the members
decided to form a sub-branch for Physics Education Research. It should be noted
that a substantial portion of physics education research has been devoted to
studying student conceptual understanding of topics in physics. Also of note is the
recent increase in articles pertaining to theories of learning. However most research
has focused on the area of mechanics and to a lesser extent electricity, magnetism,
heat and optics. The amount that has been devoted to quantum physics is quite
small.
The physics education literature associated with quantum physics published
in the period 1970 to present can be categorised into four main types of articles.
These could be broadly described as History, philosophy and interpretation of
quantum mechanics; Teaching of specifics concepts - Ideas and methods for
teaching quantum concepts, including isolated computer simulations; Teaching
materials - Packaged teaching and assessment modules; and Education research.
The associated reference lists are as complete as possible. In Appendix 9 Quantum
Physics Literature Survey, the papers have been categorised and grouped into the
following structure (see over page).
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HISTORY, PHILOSOPHY AND INTERPRETATION
OF QUANTUM MECHANICS
Quantum Physics - History
Quantum Physics - Philosophy & Interpretation
TEACHING OF SPECIFIC CONCEPTS
Quantum Physics - Teaching Concepts
Quantum Mechanics - Lecture Demonstrations & Laboratory
Quantum Physics - Computational
Quantum Physics - Tests
TEACHING MATERIALS
Quantum Physics – Computer & Book based Course Material
Quantum Physics – Courses and comments
Quantum Physics - Textbook Review
EDUCATION RESEARCH
Quantum Physics - Education Research
Related education research on waves
2.3.2 Physics – History, Philosophy and Interpretation of Quantum
Mechanics
The physics and physics education journals contain many historical
accounts that cover both the lives of the physicists, the theories they developed,
philosophical debates and discussions concerning the interpretation of quantum
mechanics. Although these are not directly aimed at addressing educational issues
they are an important resource component accessible to both teachers and students.
2.3.3 Physics – Teaching of Specific Concepts
The majority of physics education publications dealing with quantum
mechanics over the last 25 years predominately provided useful teaching materials
outlining the authors’ thoughts concerning the manner in which an idea, topic or
concept can be successfully presented. These articles, as do those in chemistry,
generally conclude that the material would enhance a student’s understanding of
the quantum concepts but make very few references to supporting education
research. It is also noted that half the physics articles listed do not have conclusions
or summaries that describe the outcomes one might expect from utilising the ideas
presented. A representative example of a paper entitled “Quantum Mechanics
made Transparent” (Henry, 1990) is outlined below:
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The article is described as a ‘sampler’. It shows “...how quantum mechanics
may be presented to students in a way that makes apparent how natural quantum
mechanics is as a description of the world... the basic ideas of quantum mechanics are
developed from intuitive first principles to the point where one can connect with the more
traditional treatments of quantum mechanics.”.
The article then uses a Socratic dialogue between a teacher and his students
which centres around a very detailed question and answer session.
The
conversation begins with a discussion of the postulates and leads into the
uncertainty principle. The discussion then moves on to cover the development of
the mathematical machinery associated with Hilbert Space and the idea of
representing observables by operators. The terms ‘eigenstates’ and ‘probability
amplitudes’ are discussed and each of the operators commonly used are presented.
The author does not provide a summary or conclusion to the article.
A small number of articles describing selected lecture demonstration and
experimental apparatus appropriate to quantum mechanics have been published.
These articles provide a description of the apparatus, associated theory and
comment on its usefulness in an educational delivery context. A comprehensive list
of demonstrations and experiments is available and the primary information source
for these is available from Physics Instructional Resource Association3 PIRA.
The advent of low cost semiconductors and programmable calculators in the
mid 1970s spawned a series of papers describing how these could be used to
generate graphical representations of quantum phenomena.
Some examples
include “The analogue computer as an aid to teaching elementary quantum mechanics”
(Summers, 1976), an article which describes how analogue techniques can be use to
tackle simple quantum mechanical problems; “Fundamental quantum mechanics graphical presentation” (Wise & Kelley, 1977), provides a selection of computer
generated displays including a computer simulated diffraction experiment, a
derivation of the uncertainty relation, and several spatial distributions of
momentum amplitudes and “Simulations of quantum-mechanical measurements with
programmable pocket calculators” (Summers, 1978), which provides the reader with
the mathematics and the code for the implementation of numerical integration and
The Physics Instructional Resource Association
http://physics.csufresno.edu/pirapub/default
3
PIRA
WEB
site
at
URL
18
gives the example of a quantum isolator. These early papers and programs paved
the way for quite sophisticated simulation software packages that were developed
and distributed after the advent of the modern personal computer.
2.3.4 Physics – Teaching Materials
Packaged teaching and assessment modules
At the commencement of this research project there were three large and
two smaller computer assisted learning (CAL) packages currently available for
teaching tertiary level quantum physics. These were:

Software Teaching of Modular Physics (SToMP) - a project funded under the
teaching and learning technologies program (TLTP). Coordinated by Dr RA Bacon,
Physics Department, University of Surrey, Guildford

Simulations in Quantum Mechanics - Consortium for Upper Level Physics
Software (CUPS) produced by J.R. Hiller, I.D. Johnston and D.F. Styer.

Quantum Mechanics on the Personal Computer - developed by S Brandt and
H.D. Dahmen (Berlin Springer).
and

Visual Quantum Mechanics - Explorations of the Quantum world for NonScience Students, Physics Department, Kansas State University

Understanding the Unobservable - a reconstruction of First Year Quantum
Physics for Engineers and Scientists by Andrew Cheetham and John Rayner,
University of Canberra
Although these packages had been reviewed by journals4 the quantum
physics components appear to have been developed without reference to education
research material.
Since the commencement of this research project the Visual
Quantum Mechanics team headed by Dean Zollman has significantly developed and
has been guided by internal and external education research.
2.3.5 Physics – Education Research
The following papers have been selected and are representative of the major
quantum mechanics education research programs. Please refer to Appendix 9 for a
complete literature review.
For articles referring to these and other CAL & video refer to the software clearinghouse
UniServe Science WEB site at URL http://www.usyd.edu.au/su/SCH
4
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In 1991 a research team at the Free University of Berlin, Germany, headed by
Helmut Fischler and Michael Lichtfeldt, presented a paper “Learning Quantum
Mechanics” at the International Workshop for Research in Physics Learning :
Theoretical Issues and Empirical Studies, held at the University of Bremen (March
4-8, 1991). This was the first published research article to investigate into students’
conceptions and their learning processes in relation to quantum mechanics.
The article reports on findings from a study that compares a teaching unit
that avoids the use of mechanical models commonly presented in texts with a
control group.
The premise was that clinging to a historically orientated
development of the subject means the teaching will also cling to the conceptions of
classical physics. The researchers propose that these mechanical models will set up
additional obstacles to understanding quantum physics.
The teaching unit was trialled at several high schools in eleven physics
courses (150 students). The study consisted of an evaluation questionnaire; video
recordings of 32 lessons across six courses, in order to discover correlations between
student conceptions and their answers given in lessons; pre-interviews for two
courses, to find out what conceptions the student had at the beginning of the
teaching unit; a post questionnaire five to six weeks after course; and postinterviews of three courses. In addition the same pre- and post- questionnaire was
administered to a control group of students in a further 14 courses (120 students).
The range of topics covered by the questionnaires and interviews was —
light, atom-electron, particle-body and students’ ideas on the philosophy of science.
The questions took the form of open-ended free answer (eg. What is light really?)
and word pair associations. The verbal answers were transcribed from videotapes.
The study yielded results covering an overview of the students’ conceptions
before and after the teaching unit and a comparison between the test and control
groups; and case studies for individual students providing conceptual maps that
summarised the students’ network of ideas.
The article’s summary section provides an illustration of the results based
upon the examples provided in the results section. Referring to the test group, ”A
teaching concept, for example like the one here, which in the first stage of planning already
considers in detail possible conceptions of students, and consciously provides room for these
conceptions to develop in the physics course, will achieve an increased cognitive conflict
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situation which will then lead the students to grapple with the subject matter in an
intensified manner. In this way the students became conscious of their own conceptions and
began to question them”.
Whereas the results from the control group tended to
incorporate the “new” phenomena into the “old” mechanistic ideas. “Here, the
different ideas in quantum physics were merely acquired verbally in the science language
level and forgotten again afterwards.”
Fischler and Lichtfeldt published a second paper entitled “Modern Physics
and Students’ Conceptions” (Fischler and Lichtfeldt, 1992) the article extends upon
the previous analyses and quantifies the “Change of students’ conceptions of an
atom’s stability” and provides “Comparisons of conceptual change between the test
and control groups”.
The article, “Common misconceptions regarding quantum mechanics”
(Styer, 1996), Daniel Styer presents fifteen preconceptions that students can have
concerning quantum mechanics. The article’s content has been drawn from his own
experiences and covers misconceptions relating to the idea of quantal state,
measurement and identical particles.
Styer points out that misconceptions are
operational as well as conceptual and recommends a variety of ways to utilise the
presented material.
These include guided discussions, essay questions and
diagnostic examinations.
Reflecting the increasing interest in educational aspects of quantum
mechanics during the period of this research two conferences have held dedicated
sessions. The first was at the 1999 NARST Annual Meeting - Looking Forward,
Looking Backward : Reflections on the Future and Past of Science Education Boston
with a session entitled “Research on the Teaching & Learning of Quantum Science”
where eight poster papers were presented.
The second was the 2002 Gordon
Conference -Physics Research and Education: Quantum Mechanics, Mount Holyoke
College, South Hadley MA, where twenty six papers were presented covering the
following areas of physics education research and developing curricula, quantum
mechanics curricula and teaching quantum mechanics, research experiments in
quantum curriculum, student understanding of physics concepts, theoretical
research and teaching quantum mechanics, topics in quantum mechanics, photon
experiments with undergraduates, quantum curricula, experimental research that
could influence quantum curricula.
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2.4 IN RELATION TO CURRENT INVESTIGATION
The quantum mechanics education research literature review shows that
very little formalised research had been undertaken by either the Chemistry or
Physics education research communities by the commencement of this project in
1997. During the intervening period 1997-2003 a number of concurrent related
studies concerned with aspects of visualisation, understanding of the wave nature
of matter, student views and conceptions have been reported. The area of focus of
the current investigation, mainly the isolation of key concepts, identification of
learning difficulties, exploration of the role of mathematics, and the exploration of
visualisation and analogy in learning quantum mechanics in relation to 2 nd year
undergraduate through to postgraduate has essentially no associated research
literature.
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CHAPTER 2 - REFERENCES
Fischler, H., Lichtfeldt, M., (1990) Learning Quantum Mechanics, ?
Proceedings of the International Workshop for Research in Physics Learning : Theoretical
Issues and Empirical Studies, University of Bremen (March 4-8, 1991). 240-258
Fischler, H., Lichtfeldt, M., (1992) Modern physics and students’ conceptions,
International Journal of Science Education, 14(2), 181-190
Haendler, B.L., (1982) Presenting the Bohr Atom, Journal of Chemical Education, 59(5),
372-375
Henry, R.C., (1990) Quantum mechanics made transparent, American Journal of
Physics, 58(11), 1087-1100
Keig, P.F., Rubba, P.A., (1993) Translation of Representation of the Structure of
Matter and its Relationship to Reasoning, Gender, Spatial Reasoning, and Specific
Prior Knowledge, Journal of Research in Science Teaching, 30(8), 883-903
Styer, D.F., (1996) Common misconceptions regarding quantum mechanics,
American Journal of Physics, 64(1), 31-34
Summers, M.K., (1976) The analogue computer as an aid to teaching elementary
quantum mechanics, Physics Education, 11(4), 296-302
Tsaparlis, G., (1997) Atomic Orbitals, Molecular Orbitals and Related Concepts:
Conceptual Difficulties Among Chemistry Students, Research in Science Education,
27(2), 271-287
Wise, M.N., Kelley, T.G., (1977) Fundamental quantum mechanics – a graphic
presentation, American Journal of Physics, 45(4), 384-394
Note: For a comprehensive categorised literature bibliography covering quantum
mechanics please refer to Appendix 8 for a Quantum Chemistry Literature Survey
and Appendix 9 for a Quantum Physics Literature Survey.
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CHAPTER 2 ........................................................................................................................................11
QUANTUM MECHANICS LITERATURE REVIEW .........................................................................11
2.1
INTRODUCTION ................................................................................................................11
2.2
CHEMISTRY RELATED ......................................................................................................11
2.2.1
2.2.2
2.2.3
2.3
2.3.2
2.3.3
2.3.4
2.3.5
2.4
Chemistry – History & Teaching of Ideas and Concepts Papers ....................................................12
Chemistry – Education Research Papers ........................................................................................13
Chemistry – Papers .........................................................................................................................14
PHYSICS RELATED ............................................................................................................15
Physics – History, Philosophy and Interpretation of Quantum Mechanics .....................................16
Physics – Teaching of Specific Concepts .......................................................................................16
Physics – Teaching Materials .........................................................................................................18
Physics – Education Research ........................................................................................................18
IN RELATION TO CURRENT INVESTIGATION ............................................................... 21