Volume 40, Issue 2, February 1972
 PAPERS


Measurement of the Magnetic Properties of Superconductors
View Description Hide DescriptionAn advanced undergraduatelaboratory experiment is described that employs a variation of the superconducting flux pump and commercially available magnetometer to measure the critical temperature,transition width, and the Meissner effect in type I superconductors in small external magnetic fields. The experiment is intended as an introduction to lowtemperature techniques and to the magnetic properties and uses of superconductors.

On the “Derivation” of Einstein's Field Equations
View Description Hide DescriptionAn attempt is made to clarify the physical and the mathematical reasonings that underlie Einstein's laws of gravitation. It appears that only by a mixture of physical reasonableness, mathematical simplicity, and aesthetic sensibility can one arrive at Einstein's field equations. The general theory of relativity is in fact an example of “the power of speculative thought.” The topics considered include a discussion of the principle of equivalence and the view of spacetime as a geometric manifold. Two “derivations” of Einstein's equations are given: one based on physical reasonableness and the other based on a variational principle and mathematical simplicity.

Computer Augmented Physics Lab
View Description Hide DescriptionA computer augmented physics lab has been developed for the thirdquarter introductory physics course in wave motion, sound, and light. New experiments are designed with application to interesting phenomena of the real world. The speed of sound and its temperature dependence are measured using timeofflight techniques. Phenomena of reflection, refraction, diffraction, and anomalous propagation (mirage) are studied using the HeNe laser. The computer is used to process and analyze experimental data and to extend experimental observations through simulation.

Relativity in an Undergraduate Laboratory—Measuring the Relativistic Mass Increase
View Description Hide DescriptionA method is described for measuring the relativistic mass increase using simple, inexpensive equipment. The effect is large and easily seen.

The Hall Effect in a Flowing Electrolyte
View Description Hide DescriptionThis experiment demonstrates that a charged particle moving through a magnetic field experiences a force . When a saltwater solution flows through a magnetic field, the positive and negative ions are separated by the Lorentz force and establish an electric field. This field is measurable by means of the potential, or Hall voltage, developed across the flow tube.

A Quantum Equation of Motion with Higher Derivatives
View Description Hide DescriptionThe problem of how to obtain a quantum equation of motion with higher derivatives is discussed. First the basic ideas of generalized classical mechanics with higher derivatives are reviewed. The generalized canonical conjugate momenta and a function , corresponding to the Hamiltonian function, are constructed. Then certain reduced momenta are introduced, which in absence of higher derivatives are identical to the canonical conjugate momenta. The function is expressed in terms of the reduced momenta. In order to obtain a quantum equation of motion, the reduced momenta in are replaced by operators fulfilling some given conditions; thus the corresponding operator can be identified with the Hamiltonian operator. With its help, and introducing a wave function, the quantum equation of motion with higher derivatives is obtained.

The Hamiltonian of a Charged Particle in a Rotating Frame
View Description Hide DescriptionThe transformation of the Hamiltonian of a charged particle from an inertial frame to a rotating frame in the presence of external electromagnetic fields is discussed.

A Teaching Strategy to Develop Physicist's Skills Early
View Description Hide DescriptionAiming to develop from the introductory courses what can be called “physicist's skills,” we have employed a teaching strategy consisting mainly of independent study and small groups constantly supervised by the teaching staff. The Berkeley Physics Course is used as textbook, complemented with several laboratory experiments seeking the “discovery” rather than verification of physical laws.

Vibrations of a Lattice Including Defects: Laboratory Demonstrations Using Electrical Analogs
View Description Hide DescriptionSimple inexpensive electrical analogs are described that illustrate the qualitative and quantitative behavior of wave motion on a onedimensional monatomic lattice, a diatomic lattice, and on a lattice containing a defect.

An Undergraduate Experiment in FourierTransform Spectrometry
View Description Hide DescriptionThe construction, theory, and application of a simple Fouriertransform spectrometer for an undergraduate student laboratory experiment are described and illustrated. The instrument is a modified, commercially available, inexpensive Michelson interferometer, and the Fourier transform is produced by a timeshared computer, using a program inbasicbased on the CooleyTukey fastFouriertransform algorithm.

Cumulative Experiments in the Advanced Laboratory
View Description Hide DescriptionAn advanced laboratory course for physics seniors is described that uses openended projects organized in such a way that all of the students work on each project in turn. The students change every two or three weeks from one project to another, each time being confronted with an ongoing experiment to which they are asked to make their contribution. The laboratory notebooks contain the cumulative total of a group effort. Individual experiments can be carried to considerable depth, but at the same time the individual students are not confined to the limitations of working on just one project.

Bringing Modern Research Techniques to a Freshman Electricity and Magnetism Laboratory
View Description Hide DescriptionThe laboratory portion of a onesemester freshman electricity and magnetism course is described. As the principal feature of the laboratory, the students built multiwire proportional counters and used them to measure the value of for 1MeV electrons.

Introducing Electron Creation and Annihilation Operators in Solid State Physics
View Description Hide DescriptionA brief and simple introduction to the theory of many electron systems that is suitable for undergraduates is given. By considering only three electrons it is possible to write out all the results explicitly. The manipulations of both determinantal wavefunctions and wavefunctions in the number representation are considered, and the electron annihilation and creation operators are defined. It is then shown how the Hamiltonian for electrons is written in second quantized form.

A Simple Procedure for Computing Density of States Spectra in Solid State Physics
View Description Hide DescriptionThe histogram method for computing density of states spectra is simplified considerably for the cubic lattices. As an example we treat the fcc lattice by randomly sampling a cube in k space (composed of octants from two adjacent WignerSeitz cells of the reciprocal lattice). Graphical results for the magnitude of the group velocity are used to locate the critical points that cause the singularities in the density of states. Illustrations are given that show how this can be used to improve the resolution of singularities that are not clearly resolved by the histogram method. A utility dispersion relation has been used for the examples, and it can be applied to spin waves as well as to electrons in the tightbinding approximation. Students can gain much insight into solid state research from this method since it helps to bridge the gap between the standard textbook treatments and the highly technical discussions of the research literature. The authors have used this method in a detailed study of the spectra of fcc lattices that will be presented elsewhere.

Laboratory Construction of Multilayer Dielectric Mirrors for HeNe Laser Applications
View Description Hide DescriptionA simple, low cost, evaporationmonitoring system for producing highly reflective, multilayerdielectricmirrors suitable for use with a heliumneon laser is described. Seventeen layer mirrors with reflectivity exceeding 99% have been constructed. Practical considerations such as substrate surface preparation and prevention of water absorption by the evaporated layers are discussed.

Matrix Elements of the Quadratic Stark Effect on Atoms with Hyperfine Structure
View Description Hide DescriptionThe perturbation of atomic hyperfine levels by a weak uniform static electric field is discussed. For nearly all atoms, the effects linear in the field are identically zero, and the levels suffer small shifts proportional to the square of the field. The calculation of these shifts using ordinary secondorder timeindependent perturbation theory is presented. The advantages of separating the interaction into kinematical and dynamical parts and techniques for performing the separation are discussed. The algebra of irreducible spherical tensors is used to separate the interaction into parts having monopolar and quadrupolar symmetry. Some numerical values of the matrix elements of the quadrupole part are given (the monopole elements are trivial), and the shifts of the hyperfine levels due to this interaction are plotted as a function of field for some typical atoms.

TeamTeaching Freshman Physics
View Description Hide DescriptionTeam teaching, in which two or more instructors share responsibility for the same class section, is being increasingly adopted in elementary schools and is already familiar to physicists in the film and television presentations of Ivey and Hume. For several years we have been utilizing team teaching as a method of handling large university freshman classes. The system appears to have several advantages, provided that the two professors have a compatible outlook on physics: (1) Since the professors share administrative responsibility for such activities as tutorials and laboratories, these can be well integrated with the lectures; (2) the dialog between the two professors seems to create a sense of participation and rapport with the class; (3) any mistakes or obscurities in one professor's presentation are immediately cleared up (in a diplomatic way) by the other; (4) the change in pace provided by the two lecturers enlivens and lightens the course; (5) the interaction of the two professors tends to generate enthusiasm, fresh viewpoints, and greater care in lecturing, all of which is felt by the class. Student reaction has been highly favorable.

The Isochronous Problem inside the Spherically Uniform Earth
View Description Hide DescriptionThe isochronous problem is worked out assuming that a particle oscillates along a constraining curve inside the spherically uniform Earth. This modification of the usual isochronous problem becomes complicated due to (1) the force acting on the particle is not unidirectional; (2) the curve of constraint must have its endpoints on the Earth's surface. A set of parametric equations satisfying the condition of isochronous motion are obtained. Then the values of these equations that are permitted by the second condition mentioned above are calculated and presented in a graph. The calculation shows that, in addition to the familiar straight line along which the particle oscillates isochronously inside the Earth, there are many curves that satisfy the conditions. The frequencies of the isochronous oscillation along these curves are simply related to the frequency along the straight line. Thus the problem treated here also has application to the Brachistochrone problem that is similarly modified.

Spectral Analysis Using a Camera
View Description Hide DescriptionA grating in front of a camera can be used as a spectrograph in an introductory physics laboratory. The student obtains a permanent record of the spectra of various elements, and using a grating equation and also a calibration curve, wavelengths can be found with sufficient precision to identify unknown sources. The precision of the methods described allows the student to obtain much greater accuracy than usually obtained with a grating spectrograph at the introductory level.

Thermodynamic Description of Materials at High Pressures
View Description Hide DescriptionA technique is presented for deriving the caloric equation of state for materials at high pressures. An incomplete equation of state, giving pressure as a function of density and energy, is used as input to a partial differential equation for entropy. The incomplete equation of state is usually inferred from shockwave experiments. The entropy equation can be solved, provided sufficient initial data are available. The technique is illustrated by two examples, a polytropic gas and a MieGruneisentype material.
