Volume 31, Issue 4, April 1963
Index of content:
31(1963); http://dx.doi.org/10.1119/1.1969423View Description Hide Description
Prepared at the request of the AAPT Committee on Resource Letters.
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, Amherst, 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 17, New York. When ordering, request Resource Letter SO-1, and enclose a stamped return envelope.
31(1963); http://dx.doi.org/10.1119/1.1969424View Description Hide Description
The Fokker-Planck approximation to the interaction term in the Boltzmann transport equation is discussed. For the case of binary collisions a simple derivation of this term is presented. The resultant expressions for the associated quantities and are evaluated for the case of a fully ionized gas. Several forms of the distribution function are considered.
31(1963); http://dx.doi.org/10.1119/1.1969425View Description Hide Description
It is shown that subject to very general conditions which do not exclude strong or velocity dependent interactions but which tend to restrict consideration to systems having only long range forces, the most probable distribution of an assembly of interacting particles is classically given exactly by a Boltzmann distribution in which appears in the Boltzmann factor a term identical to an interaction with the associated most probable self-consistent field.
31(1963); http://dx.doi.org/10.1119/1.1969426View Description Hide Description
The Lorentz force law and Maxwell's equations are extended to include magnetic as well as electric charges, by requiring that the equations be symmetrical in these charges. This extension predicts that the absolute magnetic charge of a particle cannot be detected. What can be detected are differences in magnetic charge between elementary particles and the validity of the assumed method of extending the Maxwell-Lorentzequations. An experiment is described which appears to measure the magnetic charge of an electron, but which instead bears on the form of the Maxwell-Lorentzequations. Other arguments limit the difference between proton and electron magnetic charges.
31(1963); http://dx.doi.org/10.1119/1.1969427View Description Hide Description
The construction and operation of a linear air trough, a device for floating small rectangular blocks (called gliders) on an air film, is described. The apparatus is useful for demonstrations and laboratory study of one-dimensional particle mechanics. The very small friction that is present is due to the viscosity of the air film, and causes the speed of a glider to decay with a time constant of the order of a few hundred seconds. A type of bumper has been designed which yields a coefficient of restitution greater than 0.99. Ten of these air troughs have been used in a student laboratory for a year, and have proved quite successful in experiments involving Newton's laws, collisions, damped harmonic motion, and motion on an incline.
31(1963); http://dx.doi.org/10.1119/1.1969428View Description Hide Description
It is shown that the condition of finiteness at the origin, usually imposed on solutions to the nonrelativistic Schrödinger equation for the hydrogen atom (and some other systems) is not necessary. The quadratically integrable “anomalous” solution which is usually excluded in this fashion is not a solution to the Schrödinger equation at the origin, and consequently does not need to be excluded by a boundary or other type condition. The relativistic generalization through the Dirac equation of this anomalous solution is not quadratically integrable. The solution generalized according to the relativistic Schrödinger equation is quadratically integrable and obeys the equation at the origin. Consequently, a boundary or other type condition may still be needed in a general relativistic theory.
31(1963); http://dx.doi.org/10.1119/1.1969430View Description Hide Description
The Lorentz-Einstein transformations are obtained by a method which enables one to derive a coordinate transformation between an inertial frame of reference and a noninertial accelerating system. With the aid of this transformation, one computes the explicit time for the round trip of the noninertial twin who leaves the inertial twin with initial speed , and returns by means of an acceleration. It is found that the accelerating twin returns younger than the inertial twin.
31(1963); http://dx.doi.org/10.1119/1.1969431View Description Hide Description
A simple proof is given of the fact that the ground state of a central potential is an S state. The ordering of the bound states of a central potential according to the value of the angular momentum and the number of nodes of the solution to the radial Schroedinger equation is also discussed.
31(1963); http://dx.doi.org/10.1119/1.1969432View Description Hide Description
A geometrical method for solving relativistic particle kinematics is presented. The method is especially useful for obtaining the energy and momentum distributions in a two-particle system, and the threshold energy for particle production. Energy and momentum distributions in a many-particle, system are also discussed.
31(1963); http://dx.doi.org/10.1119/1.1969433View Description Hide Description
An instructive problem in the geometrical optics of caustics is afforded by the classical theory of the rainbow. Since any caustic may also be viewed as a cusp locus of wavefronts, the same problem has bearing on certain aspects of the diffraction theory of the rainbow. Using a method of caustic analysis capable of delineating the complete emergent caustic of the primary rainbow, it is shown that past conceptions of the full caustic locus have been markedly in error. The correct locus is found to exhibit an odd cusp on a segment of the (virtual) caustic lying wholly within the raindrop.
31(1963); http://dx.doi.org/10.1119/1.1969434View Description Hide Description
It is shown that the covariance problem of the classical electron cannot be divorced from the self-stress problem as claimed recently by Rohrlich. The basic invariance principle of a relativistic fieldtheory (i.e., the formalism should be independent of the choice of the family of space-like hypersurfaces) is used to give another derivation of von Laue's theorem. This new derivation makes it quite clear that the energy-momentum expressions calculated from the Maxwell energy-stress tensor are surface dependent because of the nonvanishing of the self-stress. The fact that the early workers obtained the well-known factor of in the momentum expressions for one choice of surface, and Rohrlich and others find a factor of unity for another choice of surface, merely serves to confirm the violation of the basic invariance principle. Some additional remarks are made about the covariance problem of classical electrodynamics. The advantages and implications of the alternative proposal of Poincaré are elucidated.
31(1963); http://dx.doi.org/10.1119/1.1969435View Description Hide Description
A method of propulsion commonly used in toy boats consists of a shallow chamber, covered by a thin diaphragm, which is connected to the water astern of the boat by pipes. Filling the chamber with water and then heating it's base leads to vigorous self-induced vibration of the diaphragm and water column in the pipes with resulting forward motion of the boat. The paper describes the mechanisms of self-induced vibration and of propulsion. It is shown that this inexpensive toy demonstrates a number of physical principles and provides opportunities for further research.