摘要:

By using various general theorems, differential equations for the energy are written down for Klein–Gordon and Dirac hydrogenic atoms. When coupled with the fact that in the nonrelativistic limit one must get the Bohr formula, these equations are shown to determine the exact energy eigenvalues. Also, in the case of the Klein–Gordon equation, a recursion relation is derived from which the average values of powers of the radius can be found.

ISSN:0002-9505    

DOI:10.1119/1.10466

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

A simple microwave interferometer capable of measuring small phase shifts is described. The interferometer can easily be incorporated in an undergraduate laboratory. The interferometer is used to determine the relative refractive indices of gases to within a few parts per million. Analysis of the reflection in the test chamber can provide an interesting extension to the usual treatment of multiple reflections.

ISSN:0002-9505    

DOI:10.1119/1.10487

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

In this study of the twin paradox, the periods of acceleration necessary for the astronaut to start the journey, turn around, and return to rest at the starting point are investigated. Each twin sends a light beam of frequencyf0to the other one. The waves received by each twin have a constantly changing Doppler‐shifted frequency due to the astronaut’s acceleration. The stay‐at‐home twin (SAHT) receivesKcycles sent by the astronaut and the astronaut receivesK′ cycles sent by SAHT, whereK≠K′.KandK′ are calculated by integrating the observed instantaneous frequency with respect to time. Then the time for the round trip recorded by the astronaut,TA, and by SAHT,TS, can be compared, whereTA=K/f0andTS=K′/f0. The relationships derived are identical to those obtained by using the concept of proper time. The results are illustrated with numerical examples.

ISSN:0002-9505    

DOI:10.1119/1.10488

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

Two main questions arise when one seeks to explain the propagation of light in a dielectric medium: (i) Why does the wave slow down? (ii) Why is there apparently only a forward wave? There is a subtle answer to these questions provided by the Ewald–Oseen extinction theorem, but the physical mechanism involved is not very easily visualized. This article sets forth a simple one‐dimensional model of parallel polarizable slabs that makes the mechanism clear and links the two questions in an interesting way.

ISSN:0002-9505    

DOI:10.1119/1.10489

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

After a criticism of the emphasis put on the invariance of the speed of light in standard derivations of the Lorentz transformation, another approach to special relativity is proposed. It consists of an elementary version of general group‐theoretical arguments on the structure of space–time, and makes use only of simple mathematical techniques. Theprincipleof relativity is first stated in general terms, leading to the idea of equivalent frames of reference connected through ’’inertial’’ transformations obeying a group law. Thetheoryof relativity then is constructed by constraining the transformations through four successive hypotheses: homogeneity of space–time, isotropy of space–time, group structure, causality condition. Only the Lorentz transformations and their degenerate Galilean limit obey these constraints. The role and significance of each one of the hypotheses is stressed by exhibiting and discussing counterexamples, that is, transformations obeying all but one of these hypotheses.

ISSN:0002-9505    

DOI:10.1119/1.10490

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

A new approach to teaching the principles of quantum mechanics is presented that leads quickly to the Hilbert space postulates. After convincing the reader that an algebra of observables is a useful way to describe probabilistic observations, the paper introduces an evolution operator and demonstrates that it cannot commute with position observables. This fact, plus elementary assumptions about the possible form of the evolution operator, are sufficient to demonstrate that, if the deterministic limit of the theory is to yield Newton’s law, the evolution operator must have the familiar form of the Hamiltonian: essentially kinetic energy plus potential energy.

ISSN:0002-9505    

DOI:10.1119/1.10491

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

A simple analog computer program is described which, in conjunction with a dual‐trace storage oscilloscope, can demonstrate traveling and standing waves, the effect of various reflection coefficients, standing wave ratios, and other wave phenomena. The voltages generated by the analog are viewed on the oscilloscope screen to provide a vivid, easily understood, controllable demonstration, ideally suited for teaching.

ISSN:0002-9505    

DOI:10.1119/1.10467

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

A straightforward method is given for determining the orientation of the polar axis of an equatorially mounted optical telescope. The background theory given illustrates some important properties of the celestial sphere and gives an insight into the usual ’’rule of thumb’’ methods of axis orientation; it also provides a basis for instructors and students to devise their own orientation methods.

ISSN:0002-9505    

DOI:10.1119/1.10468

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

This paper utilizes several existing techniques in nonequilibrium statistical mechanics (in a new context) to provide a relatively simple and short evaluation of the diffusion coefficient for a Brownian particle.

ISSN:0002-9505    

DOI:10.1119/1.10469

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

A systematic procedure is presented for introducing natural units, in which physical constants such as the speed of light in vacuum, Planck’s constant, and the mass of the electron are set equal to unity. The dimensions of physical quantities are represented by vectors in an abstract linear vector space, referred to as thedimensionspace. The quantities chosen as basic units play the role of basis vectors in this space. Conversion from one system of basic units to another corresponds to a different choice of basis vectors. Such a conversion is equivalent to a linear transformation on the dimension space and may be implemented by matrix multiplication. A detailed treatment is given of the transformation from mass–length–time units to a system of natural units appropriate to the atomic domain. The broader applicability of linear algebra techniques to dimensional analysis is briefly indicated by way of conclusion.

ISSN:0002-9505    

DOI:10.1119/1.10470

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP