Quantum minds taken for a spin

Dirac's famous dictum, made immediately after the first flush of enthusiasm for the newly formulated quantum mechanics, that chemistry is now merely a matter of calculation, is still in the process of being worked through some 70 years later.

During that time, all manner of texts have sought to bring quantum mechanics to chemistry, largely by preparing young minds with the once-unfamiliar mathematics of the theory and increasingly by showing how calculations that Dirac could only shadily have anticipated (granted that a physicist can anticipate the types of problems that crop up in chemistry, are implemented on computers). Computational chemistry, the computer calculation of the electronic structure and attendant properties of individual molecules and increasingly of their aggregates as solids, can be argued to have brought Dirac's dictum to realisation, but it remains true that few of the numerous surprises of modern chemistry have been achieved by computation.

Donald Fitts's book is firmly in the stable of texts concerned with the preparation of minds rather than with the implementation of modern techniques. As such, it has to jostle for attention with many other texts that aspire to teach students (in this case, what used to be called senior undergraduate students but have now more realistically become graduate students) the foundations of quantum mechanics with an eye on the applications that are to come. In the United States, a suitable course would be the first semester of a first-year graduate course in quantum mechanics for chemists, and Fitts's text sprang from such a course.

The coverage is more or less what one would expect. It begins with the presumption that the general tenets of quantum mechanics are familiar, and proceeds with a discussion of waves, the Schrodinger equation and its simple applications. It moves on to the general principles of quantum mechanics in terms of linear operators, the harmonic oscillator, angular momentum and the hydrogen atom. The concluding chapters deal with spin, many-particle systems and approximation methods.

Those who consider that one of the illustrious triumphs of quantum mechanics is the discussion of molecular structure, will be disappointed to find that the text concludes with a cursory chapter on molecular structure, largely confined to a discussion of the Born-Oppenheimer approximation and the problem of nuclear motion. Still, the title does tell us that it is principles we are being served, rather than applications.

What makes the text stand out from the crowd? First, the firmly positioned development of wave mechanics based on a thorough discussion of wave packets in the first chapter. Second, I would identify the rigour and completeness with which the generally standard and conventional problems are presented (for instance, the factorisation method for hydrogenic atoms). Instructors who favour rigour and completeness could well find this text attractive for their courses.

P. W. Atkins is professor of chemistry, University of Oxford.