Volume 32, Issue 10, October 1964
Index of content:
32(1964); http://dx.doi.org/10.1119/1.1969851View Description Hide Description
Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.
This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Massachusetts.
Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level and the letter A indicates advanced material principally suited for senior graduate study. An asterisk (*) indicates items particularly recommended for introductory study.
Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York 10017. When ordering, request Resource Letter MB-1, and enclose a stamped return envelope.
32(1964); http://dx.doi.org/10.1119/1.1969852View Description Hide Description
The coefficients of diffusion,viscosity, and, thermal conductivity of a simple gas are calculated by expanding the distribution function in Hermite polynomials, and obtaining an approximate solution to the Boltzmann transport equation. The techniques employed result in a number of simplifications of the usual derivations.
32(1964); http://dx.doi.org/10.1119/1.1969853View Description Hide Description
The thermal and particle current densities of a gas mixture are derived by expanding the distribution functions in Laguerre polynomials and obtaining an approximate solution to the Boltzmann transport equation. The thermal diffusion factor is considered in detail. The techniques employed result in a number of simplifications of the usual derivations.
32(1964); http://dx.doi.org/10.1119/1.1969854View Description Hide Description
The variation of the Fermi energy with temperature and free-particle concentration is calculated analytically for a number of two-dimensional systems, including the free-particle gas, the intrinsic semiconductor and the impurity semiconductor. These illustrations, while, of course, applicable to certain physically realizable systems, are also of considerable illustrative and pedagogical interest, since the integrals which are involved can invariably be worked out in closed form. The Fermi energy as a function of temperature and concentration may then in some cases be calculated in closed form, while in others it is obtained implicitly as the solution to a fairly simple transcendental equation. The physical significance of the variation of Fermi energy as a function of temperature and concentration is discussed, and the deviation of the product for the two-dimensional semiconductor from the Boltzmann mass-action result is calculated and discussed in detail. The conditions corresponding to the failure of the Boltzmann approximation and the onset of degeneracy are outlined. Application of the calculational methods to simple Bose-Einstein systems is briefly treated.
32(1964); http://dx.doi.org/10.1119/1.1969855View Description Hide Description
The concepts of causality, linearity, time symmetry, unitarity, and crossing symmetry and their relation to dispersion relations are discussed. Dispersion relations are applied to some simple electrical circuits in order to illustrate some of their properties and then a simple example is given of the use of dispersion relations for the analysis of the forward angle scattering of pions on protons.
32(1964); http://dx.doi.org/10.1119/1.1969856View Description Hide Description
The current state of understanding of point defects is reviewed from the standpoint of theoretical models and experimental findings. Because of the inherent difficulties with most high-temperature equilibrium measurements of lattice defects, the experimental effort has largely been focused on the generation of excess defects by quenching, cold work, and radiation damage. The so-called five stages for the annealing of excess defects are discussed in some detail with attempt to point out where there has been substantial progress in understanding and where strong controversy still persists. Of these latter perhaps, the most outstanding example is the nature of the stage III annealing. In many cases the release of interstitials from traps at dislocations and impurities must play a role. Di-interstitial migration is a tempting possibility but recent experiments indicate a primary character for the defect mobile at this stage.
32(1964); http://dx.doi.org/10.1119/1.1969857View Description Hide Description
If a spherical potential admits bound states with a certain angular momentum, then Levinson's theorem states that , where is the scattering phase shift (corresponding to that angular momentum) as a function of energy. This is shown here by means of elementary wave mechanics.
32(1964); http://dx.doi.org/10.1119/1.1969858View Description Hide Description
The total number of complexions of an assembly of quasi-independent localized systems is equal to the sum of a large number of terms. It is usually assumed that only the greatest term in this sum makes any significant contribution to the sum. A simple way of illustrating the increasing accuracy of the assumption with increasing numbers of systems is considered in this paper.
32(1964); http://dx.doi.org/10.1119/1.1969859View Description Hide Description
Although the contributions of Sir William Rowan Hamilton to mathematical physics are well known, the physical framework for some of his major endeavors has long been neglected. A philosophical idealist, Hamilton preferred to base his conception of physical reality upon “force” or “power” rather than “matter.” Hamilton was thus drawn to the atomism of Roger Boscovich who replaced hard atoms with point centers of force. Hamilton saw his mathematical contributions as the completion of the Boscovichean model, just as Lagrange, in some sense, completed the work of Newton. Hamilton agreed in his view of matter with Michael Faraday who likewise was drawn to Boscovichean atomism but who saw it mainly in the light of his electrical and chemical researches. Joseph Henry criticized Boscovichean atomism but really was criticizing Faraday's presentation, which omitted the concept of inertia.
32(1964); http://dx.doi.org/10.1119/1.1969860View Description Hide Description
The energy levels of a one-dimensional quantum system of hard lines are obtained exactly and the resulting thermodynamic properties are evaluated by means of the grand partition function. No phase transitions occur. At high temperatures the thermodynamic properties of this system reduce to the well-known results for a classical system of hard lines.
32(1964); http://dx.doi.org/10.1119/1.1969861View Description Hide Description
In the usual development of quantum statistical mechanics the microcanonical ensemble is introduced in order to present the basic postulates of this subject with utmost clarity. However practical calculations of elementary problems using the microcanonical ensemble directly are seldom carried out. Either the method of the most probable distribution is introduced, or the canonical ensemble is introduced. Both of these methods require the development of further mathematical and physical concepts.
It is shown here that very elementary methods can be used to develop the thermodynamic properties of monatomic crystals and the “corrected” Boltzmann monatomic gas directly from the basic concepts of the microcanonical ensemble.
For more complex problems, it is shown that the microcanonical ensemble emphasizes the relation between basic concepts in statistical mechanics and certain unsolved problems in the theory of numbers.
32(1964); http://dx.doi.org/10.1119/1.1969862View Description Hide Description
This is a condensation of a paper given at the Physics Section Meeting of the American Association for the Advancement of Science in Philadelphia, 29 December 1962, by J. Theodore Peters and M. Lalevic of the Drexel Institute of Technology.
A plea is made for more colleges and universities to offer emission or atomic spectroscopy as an undergraduate elective. So much of our knowledge today of the mechanism of radiation, of atomic structure, and of properties of atomic nuclei resulted from spectroscopic research. It seems only natural then to expect more course offerings in this field. Further evidence is given for the need for more work in higher reaches of theoretical spectroscopy. There is still much to be discovered and checked and tabulated as to emission lines for many of the 102 elements.