Teaching, quantum mechanics

Quantum mechanics teaches that if the nuclei are restricted to move along the line joining them so that the possibility of rotation is excluded, the simple harmonic oscillator just considered has a single sequence of equidistant energy values the vibrational levels, given by the formula... 

Let us consider first the free atoms A. We may safely assume that they are all in the normal state since in general the states where the electrons are excited lie so high that the thermal agitation is not sufficient to lift an appreciable fraction of the atoms into them. The atoms will then only dijffer in their translational energy. We inquire How many stationary states are there with translational energy between w and w + dw if the atoms are confined to a volume V Quantum mechanics teaches that between these energy limits there are... 

Although spectroscopy and quantum mechanics are closely interrelated it is nevertheless the case that there is still a tendency to teach the subjects separately while drawing attention to the obvious overlap areas. This is the attitude 1 shall adopt in this book, which is concerned primarily with the techniques of spectroscopy and the interpretation of the data that accme. References to texts on quantum mechanics are given in the bibliography at the end of this chapter. 

It is now known that the view of electrons in individual well-defined quantum states represents an approximation. The new quantum mechanics formulated in 1926 shows unambiguously that this model is strictly incorrect. The field of chemistry continues to adhere to the model, however. Pauli s scheme and the view that each electron is in a stationary state are the basis of the current approach to chemistry teaching and the electronic account of the periodic table. The fact that Pauli unwittingly contributed to the retention of the orbital model, albeit in modified form, is somewhat paradoxical in view of his frequent criticism of the older Bohr orbits model. For example Pauli writes,... 

Eric Scerri studied chemistry at the Universities of London, Cambridge and Southampton, and obtained a Ph.D. in the history and philosophy of science from King s College, London on the question of "The Reduction of Chemistry to Quantum Mechanics," He has been a research felloiu in the history and philosophy of science at the London School of Economics and at the California Institute of Technology. He is currently an assistant professor of chemistry at Bradley University, where he also teaches histoiy and philosophy of chemistry, which are also his main research interests. He is editor of the new journal Foundations of Chemistry. Address Department of Chemistry, Bradley University, Peoria, IL 61625. Internet scerri bradley.edu. 

The use of quantum mechanics, or more specifically, orbitals and electronic configurations in teaching general chemistry is now such a widespread trend that it would be utterly futile to try to reverse it. Moreover, orbitals and configurations have been extremely useful in providing a theoretical framework for the unification of a multitude of chemical facts. 

Photo 10 Linus Pauling delivering the Richards Medal Address at Cambridge, Massachusetts, in 1947. At the left is Prof. E. Bright Wilson, Jr., who in the 1930 s collaborated with Pauling in writing Introduction to Quantum Mechanics (see SP 15), a book that is still used in teaching quantum mechanics to chemists. 

The axiomatic way of teaching quantum mechanics (QM) is anaiyzed in the light of its effectiveness in making students ready to understand and use QM. A more intuitive method of teaching QM is proposed. An outline of how a course implementing that method could be structured is presented. 

Historical prelude Kepler s laws Historical prelude Maxwell Theory Axiomatic teaching of Quantum Mechanics Problem lack of reference points Problem imprecise boundaries Problem inaccurate formulation Solution reference points from a journey Solution precise boundaries Solution accurate formulation Intuitive teaching of Quantum Mechanics Conclusion... 

A CD-ROM is attached containing a teaching course of Mossbauer spectroscopy (ca. 300 ppt frames), a selection of examples of applications of Mossbauer spectroscopy in various fields (ca. 500 ppt frames), review articles on computation and interpretation of Mossbauer parameters using modem quantum-mechanical methods, list of properties of isotopes relevant to Mossbauer spectroscopy, appendices refering to book chapters, and the first edition of this book which appeared in 1978. In subsequent printmns files are available via springer.extra.com (see imprint page). 

In the teaching of quantum mechanics, TXISolver has proved especially useful. For example. Berry, Rice, and Ross (14) give several problems on die regions of... 

There are other topics that might be considered, such as solid state theory and classical statistical mechanics. You must decide how much time to spend on each of your chosen topics. You can identify subtopics that you might omit or to which you can give only an introduction. One of the difficult decisions involves how much to teach about your own research area. You are obviously excited about this area, and will be tempted to spend too much class time on it. Another difficult decision is how much time to spend on topics of current interest such as nanomaterials and environmental chemistry. Your decisions should be guided by the composition of your class. If the class has a lot of premedical students and biochemistry majors in it, they are probably well served by a thorough treatment of thermodynamics and dynamics, and perhaps less well served by a thorough treatment of quantum mechanics and statistical mechanics. If the class is mostly composed of future chemistry graduate students, quantum mechanics and statistical mechanics are more important. 

There are a number of good choices, but you will not be completely satisfied with any textbook. 1 was not even completely satisfied when 1 used a textbook that I had written. You will probably choose a textbook that is compatible with your sequence of topics. There is at least one popular two-semester textbook that begins with quantum mechanics. (P) Most of the one-volume textbooks begin with thermodynamics but can accommodate different sequences. There are now physical chemistry textbooks that come in two or even four volumes, which provides for flexibility. In making your choice of textbook, you should consider clarity of presentation for the student. Because you are already familiar with die subject, this can be hard for you to judge. I once chose a textbook that seemed perfectly clear to me, but was not at all clear to the students. Next, you should consider the approach of the book. If you want to teach a more mathematically based course, you will probably decide to choose a textbook that uses this approach and not simply plan to provide supplementary information in class. 

Several years ago, The American Journal of Physics published an issue devoted to the teaching and learning of quantum mechanics with the expressly stated hope that the articles will help people enhance their teaching (7). In describing the articles contained in this issue, the editors stated ... 

While the authors of these papers were typically motivated to improve quantum mechanics by clarifying some particular aspect or by making the subject more palatable, their recommendations were seldom supported by any research on the teaching and learning of quantum mechanics. The trend toward research on the educational aspects of advanced topics such as quantum mechanics is a recent one (2-6). 

Fletcher, P. Johnston, I. Quantum mechanics Exploring conceptual change. Paper presented at the annual meeting of the National Association of Research in Science Teaching, Boston, 1999. 

Arguments for the presentation of kinetic theory and chemical kinetics as the first topics taught in the initial physical chemistry course are presented. This presentation allows the first topic in physical chemistry to be mathematically more accessible, to be highly relevant to modem physical chemistry practice, and to provide an opportunity to make valuable conceptual connections to topics in quantum mechanics and thermodynamics. Preliminary results from a recent survey of physical chemistry teaching practice are presented and related to the primary discussion. It was found that few departments of chemistry have adopted this order of topical presentation. 

Teaching quantum mechanics first in physical chemistry gives the properly prepared and motivated student a presentation that best represents the most active areas of physical chemistry research. A thermodynamics first approach remains most consistent with the order found in most currently used textbooks avoiding the disorientation associated with skipping around in the textbook early in the course. However, we believe that a large segment of the chemistry major... 

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