Showing papers in "American Journal of Physics in 1975"
TL;DR: In this article, the efficiency of a Carnot engine for the case where the power output is limited by the rates of heat transfer to and from the working substance was analyzed, and it was shown that the efficiency at maximum power output was given by the expression η = 1 − (T2/T1)1/2 where T1 and T2 are the respective temperatures of the heat source and heat sink.
Abstract: The efficiency of a Carnot engine is treated for the case where the power output is limited by the rates of heat transfer to and from the working substance. It is shown that the efficiency, η, at maximum power output is given by the expression η = 1 − (T2/T1)1/2 where T1 and T2 are the respective temperatures of the heat source and heat sink. It is also shown that the efficiency of existing engines is well described by the above result.
1,965 citations
TL;DR: For the case of a finite linear antenna along which a fixed current waveform propagates, the authors presented analytical time−domain solutions for the electric and magnetic radiation (far) fields.
Abstract: Textbooks rarely give time−domain solutions to antenna problems. For the case of a finite linear antenna along which a fixed current waveform propagates, we present analytical time−domain solutions for the electric and magnetic radiation (far) fields. We also give computer solutions for the total (near and far) fields. The current waveform used as an example in the computer calculations approximates that of a lightning return−stroke, a common geophysical example of the type of radiation source under consideration.
486 citations
111 citations
TL;DR: In this paper, the authors describe a simple experiment and theory for a senior level undergraduate investigation of surface plasmons in silver films, where an ∠500-A-thick film is evaporated on the hypotenuse face of a right glass prism.
Abstract: Surface plasmon phenomena are a topic of considerable current interest. We describe a simple experiment and theory for a senior level undergraduate investigation of surface plasmons in silver films. An ∠500‐A‐thick silver film is evaporated on the hypotenuse face of a right glass prism. Light (p‐polarized) from a He–Ne laser is incident through the prism on the metal film. At an angle of incidence a few degrees greater than the critical angle for total reflection, a sharp minimum in the reflected light is observed, corresponding to the excitation of the surface plasmon. The minimum in the reflectivity results from the absorption of the resonantly enhanced surface plasmon mode in the silver film. The dispersion relation for the surface plasmon and the reflectivity due to the excitation of this normal mode are calculated. Only a modest vacuum of ∠10−3 Torr is necessary to produce the required thin silver films.
95 citations
TL;DR: In this article, a derivation of the Lorentz transformation by invoking the principle of relativity alone, without resorting to the a priori assumption of the existence of a universal limiting velocity is presented.
Abstract: We present in this paper a derivation of the Lorentz transformation by invoking the principle of relativity alone, without resorting to the a priori assumption of the existence of a universal limiting velocity Such a velocity is shown to be a necessary consequence of the first postulate, and the fact that it is not infinite is borne out by experiment
91 citations
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TL;DR: In this article, examples of bouncing in one dimension and sliding down an incline are proposed for use as conceptual aids in an introductory course, where the examples of one and two dimensions for motion in a uniform gravitational field are considered quantum mechanically.
Abstract: Examples in one and two dimensions for motion in a uniform gravitational field are considered quantum mechanically. The examples of bouncing in one dimension and sliding down an incline are proposed for use as conceptual aids in an introductory course.
86 citations
TL;DR: The Editor heard Professor Heisenberg deliver the substance of this article as a lecture at Harvard University and was grateful that permission has been granted to reprint this presentation from its original source.
Abstract: Editor’s note: The Editor heard Professor Heisenberg deliver the substance of this article as a lecture at Harvard University. We are grateful that permission has been granted to reprint this presentation from its original source.
81 citations
79 citations
TL;DR: In this article, the authors investigated the nature of the forces causing the erratic motion of a knuckleball by measuring the lateral force on a baseball in a wind tunnel and identified two possible sources of a lateral force imbalance that can give rise to the observed erratic changes in the direction of a Knuckleball as it moves through the air.
Abstract: The nature of the forces causing the erratic motion of a knuckleball has been investigated by measuring the lateral force on a baseball in a wind tunnel We have identified two possible sources of a lateral force imbalance that can give rise to the observed erratic changes in the direction of a knuckleball as it moves through the air One of these results because the nonsymmetrical location of the roughness elements (strings) gives rise to a nonsymmetrical lift (lateral) force A very slowly spinning knuckleball will have imposed upon it a lateral force that changes as the positions of the strings change A knuckleball whose spin is identically zero has a constant lateral force unless a portion of the strings is precisely at a location where boundary layer separation occurs If this happens, the point of boundary layer separation switches alternatively from the front to the rear of the strings, shifting the wake from one position to another, and thereby giving rise to a second possible alternating force imbalance A two‐dimensional analysis of the trajectory of the baseball indicates that the measured force can cause a deflection of the baseball’s trajectory of more than a foot An effective knuckleball should be thrown so that it rotates substantially less than once on its path to home plate
61 citations
Journal Article•
TL;DR: In this article, the authors investigated two possible sources of a lateral force imbalance that can give rise to the observed erratic changes in the direction of a knuckleball as it moves through the air.
Abstract: The nature of the forces causing the erratic motion of a knuckleball has been investigated by measuring the lateral force on a baseball in a wind tunnel. We have identified two possible sources of a lateral force imbalance that can give rise to the observed erratic changes in the direction of a knuckleball as it moves through the air. One of these results because the nonsymmetrical location of the roughness elements (strings) gives rise to a nonsymmetrical lift (lateral) force. A very slowly spinning knuckleball will have imposed upon it a lateral force that changes as the positions of the strings change. A knuckleball whose spin is identically zero has a constant lateral force unless a portion of the strings is precisely at a location where boundary layer separation occurs. If this happens, the point of boundary layer separation switches alternatively from the front to the rear of the strings, shifting the wake from one position to another, and thereby giving rise to a second possible alternating force i...
60 citations
TL;DR: In this article, the principle of operation of phase sensitive amplifiers is discussed and three examples of the use of the phase sensitive amplifier, or "lock-in", are given, which are suitable for undergraduate laboratory use.
Abstract: The principle of operation of phase‐sensitive amplifiers is discussed. Three examples of the use of the phase‐sensitive amplifier, or ’’lock‐in,’’ are given. The examples have been chosen to be suitable for undergraduate laboratory use. The paper is concluded with the description of an inexpensive ’’student’’ lock‐in amplifier which has an overall voltage gain of 1000.
TL;DR: In this paper, the effects of the addition of a delta function potential on bound states can be computed exactly and the weak coupling limit of the implicit expression agrees with the perturbative treatment of the delta function.
Abstract: This paper presents several cases in which the effects of the addition of a delta function potential on bound states can be computed exactly. In the case of the one dimensional Schrodinger equation, a Green’s function technique is used to compute an exact implicit expression that gives the effect of the one−dimensional delta function potential on the bound states eigenvalues. It is also shown that the weak coupling limit of the implicit expression agrees with the perturbative treatment of the delta function. It is pointed out that this technique cannot be applied to obtain an exact treatment of the delta function potential δ3(r) in the three−dimensional Schrodinger equation. Instead, an alternate definition of the delta function in three dimensions as a limit of a sequence of square well potentials is used. Unlike the one dimensional case, the exact effect on the eigenvalue does not agree in the limit of weak coupling with the perturbative results. This indicates that the three−dimensional delta function potential should not be used to approximate strongly coupled short range potentials for which perturbation theory is inadequate.
TL;DR: In this paper, the problem of finding the curve of most rapid descent of a bead sliding along a wire, from one fixed point to another, under the simultaneous influence of gravity and friction, is solved.
Abstract: The problem of finding the curve of most rapid descent of a bead sliding along a wire, from one fixed point to another, under the simultaneous influence of gravity and friction, is solved. A remarkable feature of the problem is that the solution can be expressed in closed form, in terms of elementary functions.
TL;DR: In this article, it was pointed out that the definitions of instantaneous and Fourier frequencies of a signal are non-causal and their measurement requires physically unrealizable systems, and some additional definitions of frequency are given that are causal.
Abstract: It is pointed out that the definitions of instantaneous and Fourier frequencies of a signal are noncausal and their measurement requires physically unrealizable systems. Some additional definitions of frequency are given that are causal.
TL;DR: An elementary proof of Bell’s theorem on the incompatibility of local hidden−variable theories with quantum mechanics is presented, based on considerations of error rates in binary message sequences.
Abstract: An elementary proof of Bell’s theorem on the incompatibility of local hidden−variable theories with quantum mechanics is presented. The proof is based on considerations of error rates in binary message sequences.
TL;DR: In this paper, a laser beam is passed through the mixing zone of two liquids with different refractive indices, and the spatial variation of the refractive index, at different times during the mixing, can be determined from the observed deflection of the beam.
Abstract: In this simple experiment for an undergraduate laboratory a laser beam is passed through the mixing zone of two liquids with different refractive indices. The spatial variation of the refractive index, at different times during the mixing, can be determined from the observed deflection of the beam.
TL;DR: In this article, the authors discuss several volume and surface integral expressions for an electromagnetic field in the presence of a scatterer of finite extension, with special emphasis on a description of the scattering by means of a transition matrix.
Abstract: In the present article we discuss several volume and surface integral expressions for an electromagnetic field in the presence of a scatterer of finite extension, with special emphasis on a description of the scattering by means of a transition matrix.
TL;DR: In this article, the relationship between the entropy production per cycle and the thermal efficiency was investigated for a class of irreversible cyclic processes and it was shown that an increase (decrease) in an irreversible cycle's thermal efficiency does not necessarily lead to an increase in its entropy production even if the work done per cycle is held constant.
Abstract: The relationships between the entropy production per cycle and the thermal efficiency are investigated for a class of irreversible cyclic processes. Examples are given that pinpoint specific sources of irreversibility and their thermodynamic consequences. It is found that an increase (decrease) in an irreversible cycle’s thermal efficiency does not necessarily lead to a decrease (increase) in its entropy production even if the work done per cycle is held constant. Only for the case of a reversible Carnot cycle is it guaranteed that a change (negative for this case) in the efficiency is met by an entropy production change of opposite algebraic sign. Sufficiency conditions are found for which the entropy production and the efficiency η are inversely related for more general cyclic processes. For a given set of heat reservoirs and specified values of the work output W, the absolute minimum and maximum entropy productions are determined and are shown to be monotonically decreasing functions of η for fixed W. It is shown also that, for an irreversible cycle with maximum and minimum temperatures T+ and T−, respectively, η? (1−T−/T+)(1+T−ΔS/W)−1, where ΔS is the entropy production per cycle. The equality holds only for a cycle employing two reservoirs. The potential relevance of these results to environmental and technological problems is mentioned.
TL;DR: Using only Newtonia's law of gravitation and the classical expression for centripetal force, the black hole radius was derived in this paper, where the authors derived the radius of a black hole by using the AIP expression.
Abstract: Using only Newtonia’s law of gravitation and the classical expression for centripetal force, the black hole radius is derived. (AIP)
TL;DR: In this article, the completeness of the free state wavefunctions of a Hamiltonian can be explicitly checked and for certain values of the potential strength the free states prove to be complete.
Abstract: A pedagogical example is presented in which the completeness of the free state wavefunctions of a Hamiltonian can be explicitly checked. For certain values of the potential strength the free states prove to be complete. For other values of the potential strength the free states are shown to be incomplete and the extent of this incompleteness is shown to consist of precisely one function. Using the fact that the totality of all energy eigenfunctions must be complete, this single bound state wavefunction is calculated using the free state wavefunctions only.
TL;DR: Estermann was engaged in writing a book on the history of the molecular beam method when he died in Haifa, Israel on 31 March 1973 as discussed by the authors, the original plan of the manuscript was to cover three distinct historical periods: the first, the years 1911-1933, when the center of research in molecular beams was at the University of Hamburg; the second, from 1933 to the outbreak of World War II, when most active laboratory working in the field was at Columbia University; and the postwar period, when many laboratories on both sides of the Atlantic became actively engaged in
Abstract: Dr. Immanuel Estermann was engaged in writing a book on the History of the Molecular Beam Method when he died in Haifa, Israel on 31 March 1973. The original plan of the manuscript was to cover three distinct historical periods: the first, the years 1911–1933, when the center of research in molecular beams was at the University of Hamburg; the second, from 1933 to the outbreak of World War II, when the most active laboratory working in the field was at Columbia University; and the postwar period, when many laboratories on both sides of the Atlantic became actively engaged in this field. The material in this paper deals primarily with the early historical period and would have formed the essence of the first two chapters of the book. In addition to presenting interesting historical facts on a crucial period in the development of quantum physics, it contains some amusing historical sidelights on the research personalities that dominated that period.
TL;DR: In this paper, a simple problem, the one-dimensional delta function potential, through which the bound state and continuum wave function are found is illustrated by solving a simple simple problem.
Abstract: The formulation of quantum‐mechanical problems in momentum space, which is largely ignored in traditional courses but is used in research, is discussed. In particular, the formulation of scattering problems, for which the momentum representation is quite natural, is neither generally well known nor obvious. This is illustrated by solving a simple problem, the one‐dimensional delta function potential, through which the bound state and continuum wave function are found.
TL;DR: In this article, the form of the Hamiltonian in terms of the translation generators, along with the Galilei generators, for a nonrelativistic particle was determined for an irreducible unitary representation of the Poincare group, at least well enough to identify the velocity operators and thus the momentum.
Abstract: The operators −i∇, the translation generators, are related to mass and velocity by a simple argument that determines the form of the Hamiltonian, in terms of the translation generators, along with the Galilei generators, for a nonrelativistic particle. For a relativistic particle, a similar discussion is given for the analogous problem of determining the position operators for an irreducible unitary representation of the Poincare group, at least well enough to identify the velocity operators and thus identify the momentum.
TL;DR: One-dimensional models for two-electron systems resembling the helium atom and hydrogen molecule are studied using δ function potentials between all particles in this article, where the essential features of the helium atoms and hydrogen molecules ground states are exhibited by these models.
Abstract: One‐dimensional models for two‐electron systems resembling the helium atom and hydrogen molecule are studied using δ‐function potentials between all particles. It is noted that the essential features of the helium atom and hydrogen molecule ground states are exhibited by these models. The calculations are simple and useful pedagogical tools for illustrating the techniques used in more complicated and realistic calculations of energy eigenvalues and eigenfunctions.
TL;DR: In this article, it was shown that for the classical isotropic harmonic oscillator, the above procedure can lead to a piecewise-conserved Runge vector as well as to a conserved one of the same magnitude.
Abstract: A procedure for constructing a Runge vector for a particle moving (classically or relativistically) under any central force has been given by Fradkin Serebrennikov and Shabad have pointed out that such vectors may be piecewise conserved, rather than constants for the entire motion It is shown herein that, for the classical isotropic harmonic oscillator, the above procedure can lead to a piecewise‐conserved Runge vector as well as to a conserved one (of the same magnitude) We relate this ambiguity to the symmetries of the orbit
TL;DR: A theory of orbits for the inverse‐square central force law that differs considerably from the usual deductive approach, making no explicit use of calculus, and leading to a number of geometrically realizable physical invariants of the orbits.
Abstract: We develop a theory of orbits for the inverse‐square central force law that differs considerably from the usual deductive approach. In particular, we make no explicit use of calculus. By beginning with qualitative aspects of solutions, we are led to a number of geometrically realizable physical invariants of the orbits. Consequently, most of our theorems rely only on simple geometrical relationships. Despite its simplicity, our planetary geometry is powerful enough to treat a wide range of perturbations with relative ease. Furthermore, without introducing any more machinery, we obtain full quantitative results. The paper concludes with suggestions for further research into the geometry of planetary orbits.
TL;DR: In this paper, it is shown that the eigenfunctions of a particular Hamiltonian are complete for a particle moving in one dimension with a Dirac delta function potential, where the particle is considered as a single point.
Abstract: By explicit calculation it is shown that the eigenfunctions of a particular Hamiltonian are complete. The Hamiltonian considered is that for a particle moving in one dimension with a Dirac delta function potential.
TL;DR: In this article, a model of second-order phase transitions is presented, which reproduce the static behavior above a mean field phase transition and the thermodynamic slowing down on each side of it.
Abstract: We present models of second‐order phase transitions, using elementary equipment, which reproduce the static behavior above a mean field phase transition and the thermodynamic slowing down on each side of it. The model is compared to continuum physics examples involving side effects in liquid crystals (Freedericksz transition) and in superconductors (proximity effect).