Volume 46, Issue 4, April 1978
 Papers


Tunneling—how it all started
View Description Hide DescriptionA personal account of the early history of tunneling and the contribution of Ronald W. Gurney.

Teacher effectiveness: Self‐determined change
View Description Hide DescriptionThis study was designed to explore the feasibility of establishing observer‐teacher relationships at the university level and to test the usefulness of observation data to university teachers. Part I (carried out in the spring of 1972) dealt with the questions: (1) Does a teacher’s classroom behavior change after he receives systematic observation data? and (2) If so, what are the characteristics of the change? Part II (carried out in the spring of 1975) dealt with the questions: (1) Why does a teacher desire to make specific changes in classroom behavior? and (2) How does a teacher produce desired changes?

Can individual elementary particles have individual properties?
View Description Hide DescriptionAssuming the validity of conventional quantum theory, we may divide the laws of physics into laws of conservation and laws of change. The former, unmodified by quantum theory, are deterministic. The latter, according to quantum theory, are indeterministic for single systems, but curiously are deterministic for probability distributions in ensembles of particles. Elementary particles are characterized by invariant properties which are conserved. The question is discussed whether noninvariant observables, like momentum or spin components, at some chosen time can have definite instantaneous values. For investigating this, we discuss a simplified version of a thought experiment proposed some years ago by Wigner. This provides some answers to two questions: (1) In what sense is it usually insufficient to describe a beam of equally prepared particles as a collection of particles with certain given properties, instead of describing this beam by waves or by a state vector? (2) In case we know what value an observable has for a particle, when may it be useful to describe this individual particle quantum mechanically by ascribing to it the corresponding eigenfunction as its individual state vector?

Can the effect precede its cause in classical electrodynamics?
View Description Hide DescriptionIn classical electrodynamics, the imposition of Dirac’s asymptotic boundary condition on the differential equation of motion for a charged particle leads to the prediction of preacceleration; that is, the particle’s acceleration at time t depends on external forces acting at times later than t. Since force is usually considered to be the cause of acceleration rather than vice versa, the existence of this preacceleration has been taken to show that an effect can precede its cause. In this paper it is argued that such a retrocausal interpretation of preacceleration is either unfounded or false.

Derivation of Maxwell’s equations from the local gauge invariance of quantum mechanics
View Description Hide DescriptionMaxwell’sequations are derived from the principle of form invariance of quantum mechanics under multiplication of the wave function by a space‐ and time‐dependent phase factor (local gauge transformations of the first kind). The principle leads to the introduction of the vector and scalar potentials, which are shown to transform under the usual gauge transformations of electromagnetism (gauge transformations of the second kind). The electric and magnetic fields are introduced in the usual way to obtain observable fields which are gauge independent. Faraday’s law and the condition of no magnetic monopoles are obtained from the gauge transformations of the potentials. Conservation of energy and the linearity of the field equations are assumed to obtain Gauss’ law and the Ampere‐Maxwell law.

Surface effects and the density of states of electrons in a semi‐infinite array of identical potentials
View Description Hide DescriptionThe relationship between the surface effects and the boundary conditions of a semi‐infinite array of identical potentials has been studied. It is found that the appearance of the surface states hinges on the appropriate consideration of the possible effects on atoms near the surface due to the presence of the surface. Criteria for the existence of the surface states for two specific models of the surface are obtained.

Quasi‐Carnot cycles, negative Kelvin temperatures, and the laws of thermodynamics
View Description Hide DescriptionIt is maintained that the impossibility of moving a thermodynamic system adiabatically and reversibly (isentropically) from the domain of positive Kelvin temperatures to the domain of negative Kelvin temperatures (and vice versa) is a consequence of (an extended form of) the Third Law of thermodynamics and not of the Second Law alone; it is further maintained that Schöpf’s apparent proof to the contrary is inconclusive. In the course of the discussion the properties of a quasi‐Carnot cycle (two adiabatic steps coupled with two steps involving floating temperature heat reservoirs) are explored.

Relativistic two‐body electrodynamics
View Description Hide DescriptionThe few known analytic solutions for the special‐relativistic two‐body electrodynamic problem are presented. The point particles interact by relativistic action‐at‐a‐distance forces without radiation reaction, for both time‐symmetric and time‐asymmetric interactions. For ease of understanding by those not specialists in relativity, standard vector notation is used, avoiding metrics. Recipes are given for obtaining the conserved quantities, four‐momentum, angular momentumtensor, and dilation, directly from the equations of motion and without recourse to action principles.

Basic properties of certain types of operators: A unified treatment
View Description Hide DescriptionUsing normal operators as a common footing, the basic properties of Hermitian operators, unitary operators, and anti‐Hermitian operators are treated from a unified viewpoint. The interlinks among the eigenvalues of these operators are elucidated with the help of suitable prescriptions for mapping in the plane of complex eigenvalues. Further, we show that some of the characteristics of Hermitian operators hold good under a perspective which is broader than the defining criterion for Hermitian operators.

On the nature of the Hamiltonian for the interaction of radiation with atoms and molecules: (e/m c)p⋅A, −μ⋅E, and all that
View Description Hide DescriptionIn nonrelativistic quantum electrodynamics there is a class of equivalent Hamiltonians that describe a system of radiation and atoms or molecules in interaction. Three specific examples, namely, the minimal coupling, the multipolar, and the space‐translated forms are analyzed here in detail. Their equivalence is demonstrated. The Lagrangian approach has also been examined to give further insight into the dynamics. The equations of motion are compared. Finally, the process of two‐photon absorption by an atom is used as an application of the various interaction Hamiltonians in a discussion of their computational differences.

On the high‐temperature expansion of the density matrix
View Description Hide DescriptionThe high‐temperature expansion of the density matrix e ^{−βH } is derived in an elementary way, which avoids use of the Feynman‐Kac formula. The expansion provides an elementary introduction to such topics as the interaction representation, Wick’s theorem, and the functional representation of the Green’s function.

Electrostatic potential energy leading to an inertial mass change for a system of two point charges
View Description Hide DescriptionThe system of two charged point particles traveling side by side at arbitrary velocity less than the speed of light and accelerating slowly is analyzed within classical electromagnetism as to the connection between the electrostatic potential energy of the system and the inertial mass. The total external force necessary to accelerate the system is calculated, and it is found that the change of system mass associated with the electrostatic potential energy of the two particles is accounted for exactly by the electromagnetic force of one charged particle on the other during the acceleration. The example provides a striking illustration and detailed mechanism for understanding the mass‐energy idea associated with special relativity.

Baccalaureate program in medical physics
View Description Hide DescriptionOne category of applied physics presently of great interest is medical physics; in large measure this is due to the increasingly rapid transfer of physical concepts and techniques to the area of health care. The traditional entrance to the medical physics profession is at the master’s level. A four‐year baccalaureate applied physics program is described, which, among other things, provides preparation for specialized graduate study in this field. Increased material in chemistry and biology is required as well as work in radiological physics, the latter conducted partly in a hospital setting.

Simple derivation of the diffusion equation from the Fokker‐Planck equation using perturbation methods
View Description Hide DescriptionIn the paper, we develop an alternate formulation of the diffusion or Smoluchowski equation in the framework of asymptotic perturbation analysis. With the Fokker‐Planck equation as our starting point, and with the assumption of small mean free paths, an explicit scaling of the time coordinate makes this derivation especially suited for classroom use.

Esoteric elementary particle phenomena in undergraduate physics—spontaneous symmetry breaking and scale invariance
View Description Hide DescriptionWe take two rather abstract concepts from elementary particle physics, and show that there actually exist analogs to both of them in undergraduate physics. In the case of spontaneous symmetry breaking, we provide an example where the most symmetrical state of a simple system suddenly becomes unstable, while a less symmetrical state develops lower energy and becomes stable. In the case of scale invariance, we consider an example with no natural scale determined, and show that a straightforward dimensional analysis of the problem leads to incorrect results, because of the occurrence of infinities, even though they would appear to be irrelevant infinities that might not be expected to affect the dimensions of the answer. We then show how a simple use of the scale invariance of the problem leads to the correct answer.

Measurement of thermoelectric effects at low temperature
View Description Hide DescriptionA method, suitable for an advanced undergraduate project laboratory, is described whereby the existence of the Seebeck, Peltier, and Thomson effects may be demonstrated in a single experimental setup using a Cu–0.01%Fe sample. Experimental results for the Peltier and Thomson coefficients are obtained which are consistent with the Kelvin relations. The experiment provides the student with a convenient introduction to the use of liquid helium as well as to the procedural and measuring techniques employed at low temperatures.

Multipole radiation theory in an upper‐level undergraduate physics course
View Description Hide DescriptionAspects of multipole radiation theory are presented at a level suitable for a senior course in nuclear physics. Selection rules, dependence on photon energy, polarizations, and radiation patterns are treated for E1, M1, and E2 multipoles.

Particles falling in a rotating fluid
View Description Hide DescriptionParticles falling in a fluid rotating about a horizontal axis can go into quasistable orbits. An analytical solution of the particle’s motion is derived. This model may be applicable to suspension of diatoms and other particles in the ocean.

Pendulum on a massive cord
View Description Hide DescriptionThe oscillation frequency of a pendulum supported by a massive string, discussed previously by Armstrong, is analyzed both analytically and using a variational method. The variational approach displays its characteristic benefits in providing both an efficient computational procedure and also useful insight into the physical behavior of the system.

Bouncing ball experiment
View Description Hide DescriptionThe results of an analysis of two target surfaces used in a bouncing ball experiment are presented. It is shown that if a ball is dropped onto a flat surface with an initial spin, or component of velocity horizontal to the surface, the ball will travel horizontally in ’’one direction’’ while it executes multiple bounces. Because of this phenomenon, the ball will eventually fall off any reasonably sized flat target surface. To overcome this, we consider a surface with a conical depression in it so as to ’’focus’’ or localize the bouncing ball. Equations that describe the motion on such a surface are presented.
