Relegate Bohr's atom to history

Quantum Mechanics - An Introduction to Quantum Theory - Quantum Mechanics

May 2, 2003

Quantum mechanics is not only the basis of most of modern physics, it plays an essential role in chemistry and underlies much of biology. However, the fundamentals of quantum mechanics are both mathematically complex and counterintuitive, given that we have all been brought up in the "classical" world where its effects are not readily apparent. Because of this, the teaching of quantum mechanics presents many challenges and choices. Do we adopt a historical approach, in the belief that the clearest description is what evolved over the past 80 or so years, or do we ignore history in favour of what now seems the most logical and complete approach? Do we expect students to become equipped with all the necessary mathematical tools from the start or do we introduce the ideas qualitatively using simple examples and induction from what they already know? The authors of these three textbooks have answered these questions in different ways.

In the second edition of Quantum Mechanics, B. H. Bransden and C. J. Joachain "have firmly in mind students of physics rather than mathematics". Their path is traditional, starting with the experiments performed about 100 years ago that led to the new ideas. They follow history to the extent that they begin with Planck's theory of black-body radiation; this means that they have to introduce a considerable amount of classical thermodynamics and radiation physics before getting to the punchline. Their other examples, particularly the photoelectric effect and the nature of atomic spectra, seem to lead much more directly to the need for quantisation and I would sacrifice history at this point at least.

The Bohr model of the atom also makes an appearance in their first chapter, and rates a mention in both the other texts. This assumed that an electron in an atom such as hydrogen orbited the nucleus in a manner similar to a planet orbiting the sun; several largely ad hoc rules were applied to produce correct predictions for the allowed energies of the electron in its orbit, and hence the wavelengths of the spectral lines. However, other quantities - notably the electron's angular momentum - are incorrectly predicted and the model propagates a misleadingly classical picture of atomic structure. The historical development of scientific knowledge has not always been direct and progressive: dead ends such as the phlogiston theory of combustion have arisen occasionally. The Bohr model of the atom is another of these and its study should now be confined to courses in the history of science.

Louis Marchildon's approach is just about diametrically opposite to that of Bransden and Joachain; his "exposition largely develops round the central notion of state space". After a short introductory chapter, the second and third deal with finite-dimensional vector and state spaces, allowing the postulates of quantum mechanics to be developed formally.

There are not many compromises in the later sections of this book. The chapter on symmetry includes material that could form almost a whole course on the mathematics of group theory, and these ideas are built on to develop relativistic quantum mechanics and the Dirac equation. This could be a useful book for an advanced graduate course or theoretical specialists and a useful reference for others, but it is hard to imagine its being useful to the chemists, biophysicists and engineers mentioned in the preface.

The level of F. S. Levin's text comes somewhere in between that of the other two. It is "designed for use in year-long undergraduate courses...

and as a supplemental text at graduate level". Students are introduced to the concepts of photons and the wave nature of matter, but without detailed discussion of the historical experiments. Quantum mechanics is introduced though a discus-sion of the classical properties of the stretched string and the quantum properties of a particle in a box. This (perhaps unnecessarily) involves the use of a more advanced and general form of classical mechanics than is generally taught to undergraduates. The fundamental postulates of quantum mechanics are introduced in chapter four, after some of the general properties of vector spaces have been established.

The material covered in the three texts is unsurprisingly similar. As the core curriculum of the subject is established, I looked for discussions of modern applications and the conceptual basis of the subject. An example of the former is the geometric or "Berry" phase that was discovered in 1984 and later confirmed experimentally. This effect predicts that the wavefunction of a slowly changing quantum system can acquire a phase, even after it has been returned to the same conditions as it started from.

Bransden and Joachain and Levin feature the Berry phase in their respective prefaces, although only the former includes Berry in the index. I found Bransden and Joachain's treatment of this topic particularly clear.

It has become increasingly obvious over the past 20 years that the conceptual basis of quantum physics is much less clear than had generally been thought. As a result, modern texts almost invariably include some discussion of these and the current set forms no exception - although Levin's discussion is quite brief. All refer to the work of John Bell. All three are also critical of the idea that quantum systems could be usefully described by "hidden variable" theories in which reality is ascribed to a property of a quantum system (for example, the position of a particle) even in a context where this is unobservable in principle. The so-called "quantum measurement problem" also rates a mention in two of the texts (not Levin's). Marchildon includes quite a detailed account of modern work on "decoherence" and "consistent histories", which claims (unsatisfactorily in my view) to resolve the problems in this area.

In conclusion, all three books are sound reliable texts, suitable for students with the appropriate abilities and background.

Alastair Rae is reader in quantum physics, University of Birmingham.

Quantum Mechanics

Author - B. H. Bransden and C. J. Joachain
ISBN - 0582 35691 1
Publisher - Prentice Hall
Price - £34.99
Pages - 816

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