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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 Education[1] 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 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.
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-and-pencil 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, 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 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).
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:
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 Association[3] 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 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 Non-Science 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 journals[4] 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.