Volume 38, Issue 11, November 1970
 PAPERS


Conducting Spiral as an Acyclic or Unipolar Machine
View Description Hide DescriptionThis paper shows that a conducting spiral behaves as a unipolar machine. As a first approximation, the current in the spiral can be viewed as a superposition of a system of circular currents, which provide a magnetic field perpendicular to the plane of the spiral, and a radial current on which the Ampere forces produce a selftorque. An essential feature of unipolar machines is stressed, i.e., the relevant electromagnetic interactions take place between perpendicular currents and not between parallel ones, as happens in the other machines. A simplified series unipolar machine for laboratory and classroom instruction has been built and is discussed.

An Isotropic Approach to Divergence
View Description Hide DescriptionThe form of the divergence operator in rectangular coordinates is derived by use of an infinitesimal spherical volume instead of the usual cubical one. The derivation shows clearly that the expression does not depend on the orientation of axes.

Crystal Symmetry and Macroscopic Laws. II
View Description Hide DescriptionIn an earlier paper [Amer. J. Phys. 36, 735 (1968)] of the same title one of us described a particularly simple method by which symmetry considerations can be applied to determine the possible forms of macroscopic laws. In this sequel we clarify the role of timereversal symmetry, describe more fully the criteria for the occurrence of spontaneous electric and magnetic moments, discuss the application of the method to magnetically ordered systems, and correct a number of errors in the tables.

Secondary Structure in HighEnergy Scattering Amplitudes
View Description Hide DescriptionThe dependence of the highenergy largeangle scattering amplitude on the detailed shape of the partial wave distribution or impact parameter shape factor is considered. Transformations of the partial wave series and impact parameter representations are derived which make explicit the dependence on the “smoothness” of these shapes. The transformations are also used to construct examples of partial wave distributions and shape factors leading to analytic expressions for the scattering amplitude showing clearly the dependence on the “surface thickness” of the distributions.

Propagation of a Longitudinal Disturbance on a OneDimensional Lattice
View Description Hide DescriptionPropagation of a particular longitudinal disturbance on a semiinfinite onedimensional lattice of identical mass particles coupled by identical massless ideal springs is studied. With all but one of the particles at rest and all the connecting springs at equilibrium length at , the end particle is constrained to move with fixed longitudinal velocity for all . Use is made of a method in which an infinite system of differential equations of motion is replaced by a single ordinary differential equation; the timedependent Fourier coefficients of the equation's solution are the respective displacements from equilibrium of the individual lattice particles. These displacements and the corresponding velocities are expressed in terms of definite integrals. The results of velocity computations are presented along with asymptotic velocity distributions on the lattice and are discussed in relation to a simplified propagation description posited in a recent introductory textbook. The case of a semiinfinite elastic continuum subject to essentially the same initial and boundary conditions is worked out as a limit of the solution of the problem for the lattice.

A Useful Form of the Minkowski Diagram
View Description Hide DescriptionWe give a diagrammatic representation of the diagonal form of the special Lorentz transformation. The null coordinates are plotted along a single set of orthogonal axes. Special Lorentz transformations are then represented only by a change of scale along those orthogonal axes. This diagram, which we call a null coordinate diagram, and the Minkowski diagram are closely connected. To demonstrate the use of the null coordinate diagram, we apply it to the linear Doppler effect, time dilation, and Lorentz contraction.

Matrix Interaction for EPR Spectrum in a Paramagnetic Crystal under External Stress
View Description Hide DescriptionUsing a method based only in group theory, and having in mind that many of today's experiments in EPR are done with paramagnetic crystals under external stress, we want to give those starting to work with this technique some idea how to write down a complete expression for the total interaction without assuming any model such as the spin Hamiltonian. This matrix interaction will have more parameters than the spin Hamiltonian, and we will decide the contribution of each one solely by experiment. We show the results of some experiments in transition and rare earth ions, and the equivalence between spin Hamiltonian parameters and the matrix interaction one.

Possible Origins of Internal Symmetry
View Description Hide DescriptionIt is argued that the existence of the Pauli and Touschek transformations for the fourcomponent neutrino field is a simple consequence of the fact that the basic wave function is a direct sum of two elementary spinors.

Electromagnetic Momentum, Energy, and Mass
View Description Hide DescriptionElectromagnetic systems of finite mass and of zero mass are considered. For both cases the electromagnetic energy and momentum are computed and are shown to lead to essentially different formulas. An invariant expression for the electromagnetic mass in systems is derived. All results are then specialized to the electrostatic case. Historical and present day confusion in the literature is discussed.

A Variation on Melde's Experiment
View Description Hide DescriptionA modification of the conventional driven vibrating string experiment is described which makes use of steel wires of various diameters and shows the effects of the stiffness of the wire on the tension required to make the wire resonate with the driving force.

Integral Equation Formulation of OneDimensional Quantum Mechanics
View Description Hide DescriptionThe transformation of the onedimensional Schrödinger equation to an integral equation is described. Several interesting problems are analyzed using this formulation. The level of the material is such as to be appropriate for a senior level undergraduate course in quantum mechanics.

Absolutely Stable and Metastable Thermodynamic States of a Magnetic Model Exhibiting a FirstOrder Phase Transition
View Description Hide DescriptionThe thermodynamic states of a particular magnetic model are obtained in terms of the temperature, external magnetic field, and magnetic moment. The magnetic moment plays the role of the order parameter in the usual Landau theory of phase transitions. Absolute and local minima of the free energy as a function of the order parameter (the magnetization) are obtained which correspond, respectively, to absolutely stable and metastable states of the system.

Frequency Shifting of Light by means of a Kerr Cell
View Description Hide DescriptionA frequency shift was produced in a HeNe laser beam by a time dependent change in the index of refraction of a Kerr cell. The shift was detected by measuring the beat frequency obtained by combining the parallel and perpendicularly polarized components of the laser beam transmitted by the cell. A beat frequency varying between was noted.

Comparison of Correlated Wave Functions in the Helium Sequence
View Description Hide DescriptionThe method of calculating ground state energies of heliumlike atoms by use of a variational wave function is well known. The usual procedure is to start with an uncorrelated wave function multiplied by a correlation factor containing several variational parameters. The variational principle is then used to determine the parameters which give minimum energy. It has been the practice to use the same uncorrelated function and then compare the results when several different correlation factors were used. In this work, the same correlation factor is retained, and the effect of using two different uncorrelated functions is investigated. The correlation factor used was , where and are variational parameters. The uncorrelated wave functions used were hydrogenic functions and HartreeFock functions. Results are presented for the Helike ions with , and it will be seen that the hydrogenic functions give the best results when electron correlation is included.

Paragas
View Description Hide DescriptionA hypothetical gas of identical spinless particles obeying parastatistics is dealt with. The method allows a unified treatment of both the Fermi and the Bose gases. The partition function, the equation of state, and the thermodynamic functions are simple generalizations of those for the physical quantum gases, which are included as special cases. All paragases have a Fermi energy and a BoseEinstein condensation. A quantitative criterion of degeneracy for the physical quantum gases is proposed. The fluctuations of occupation numbers and density are also discussed. Expansions for high and low temperatures are given to third order.

Lippmann Color Photography for the Undergraduate Laboratory
View Description Hide DescriptionWith the advent of holography in the undergraduate laboratory and the availability of very fine grain, essentially panchromatic emulsions, it has become relatively easy to produce color photographs by the Lippmann method. An experiment developed in the advanced physics laboratory at Stanford is described here. The elementary theory of the Lippmann process is presented along with a procedure for producing monochromatic plates using a hydroquinone developer and a procedure for producing natural color plates using a pyrogallol developer.

A Coulomb's Law Balance Suitable for Physics Majors and Nonscience Students
View Description Hide DescriptionThe PSSC soda straw balance is adapted to make it applicable to a study of Coulomb's law. Because of the inherent simplicity of the balance, it is well suited to nonscience students as well as physics majors. A calculation is made to determine a correction for the redistribution of charge as conducting spheres of finite radius are brought near each other in the Coulomb's law experiment. Typical data are presented to illustrate the value of this simple balance as a teaching device.
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 NOTES AND DISCUSSIONS


Speed of Light with Laser
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Quantitative or Qualitative Use of Kinetic Theory Models
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A Simple Explanation of the Depth of Field Properties of an Ideal Lens
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