Until the beginning of this decade the number of significant exactly soluble problems in physics was limited to a very few: the classical or quanti sed harmonic oscillator, the linearised many-body problem, the quanti sed hydrogen atom, Newton's solution of the planetary orbit problem, Onsager's solution of the two-dimensional Ising problem, almost exhaust the list. Now the situation is quite different. We have a large number of exactly soluble nonlinear systems of physical significance and the number of these is growing steadily. Recent examples include a limited solution of Ein- stein's...

When, in the spring of 1979, H.P. Baltes presented me with the precursor of this vo 1 ume, the book on "Inverse Source Problems in Opti cs", I expressed my gratitude in a short note, 11hich in translation, reads: "Dear Dr. Ba ltes, the mere titl e of your unexpected gift evokes memori es of a period, which, in the terminology of your own contribution, would be described as the Stone Age of the Inverse Problem. Those were pleasant times. Walter Kohn and I lived in a cave by ourselves, drew pictures on the walls, and nobody seemed to care. Now, however, Inversion has become an Industry, which I...

When I was a student, in the early fifties, the properties of gratings were generally explained according to the scalar theory of optics. The grating formula (which pre dicts the diffraction angles for a given angle of incidence) was established, exper imentally verified, and intensively used as a source for textbook problems. Indeed those grating properties, we can call optical properties, were taught'in a satisfac tory manner and the students were able to clearly understand the diffraction and dispersion of light by gratings. On the other hand, little was said about the "energy properties,"...

No single volume has been entirely devoted to the properties of magnetic lenses, so far as I am aware, although of course all the numerous textbooks on electron optics devote space to them. The absence of such a volume, bringing together in formation about the theory and practical design of these lenses, is surprising, for their introduction some fifty years ago has created an entirely new family of commercial instruments, ranging from the now traditional transmission electron microscope, through the reflection and transmission scanning microscopes, to co lumns for micromachining and...

The growth and maturity of research in structural phase transitions (SPT) make it an appropriate subject for the Topics in Current Physics series. The maturing pro- cess is, however, by no means complete. New areas such as incommensurable SPT, quasi-low-dimensional systems, systems containing lattice disorder due to impuri- ties or as mixed crystals, multicritical points, and quantum effects have recently come under focus. The understanding of the dynamics, be it microscopic soft-mode theory or critical dynamics, more specifically the central-peak problem, is also still quite incomplete. On...

It is now ten years since it was first convincingly shown that below 1 K the ther mal conductivity and the heat capacity of amorphous solids behave in a way which is strikingly different to that of crystalline solids. Since that time there has been a wide variety of experimental and theoretical studies which have not only defined and clarified the low temperature problem more closely, but have also linked these differences between amorphous and crystalline solids to those suggested by older acoustic and thermal experiments (extending up to 100 K). The interest in this somewhat restricted...

With the advent of X-ray diffraction and crystal structure determination in 1912 researchers in physics and chemistry began investigating the problem of crystal co hesion, i. e., on the question of what holds crystals together. The names of M. Born, E. Madelung, P. P. Ewald, F. Bloch, E. P. Wigner, and J. E. Mayer are, in particular, associated with the pre-1940 work on the cohesion of inorganic lattices. The advent of digital computers brought along great advances in the detailed understanding of ionic crystals, molecular crystals, and metals. The work of P. O. Lowdin and r A. I....

In studying the radiation-matter interaction, one can take two different approaches. The first is typical of spectroscopy: one considers the interaction between radi- ation and a single atom, i. e., one studies those phenomena in which the presence of other atoms is irrelevant. The other attitude consists, in contrast, in studying those phenomena which arise just from the simultaneous presence of many atoms. In fact, all the atoms interact with the same electromagnetic field; under suitable conditions, this situation creates strong atom-atom correlations, which in turn give rise to a...

It is now a quarter of a century since Junge and his coworkers recovered the first sample from the sulfate aerosol layer in the stratosphere. Since that time vast strides have been made in determining its physical properties and morphology. These investigations have been performed with instruments on board aircraft and balloon platforms as in the early days, with ground-based lidar (optical radar), and most recently with satellite-borne optical instruments. It will become evident in Chapter 2 that in situ measurements by aircI'aft and, balloon sensors complement rather than duplicate the...