摘要:

An elementary approach to the quantum theory of angular momentum is sketched. The quantization of angular momentum components, Heisenberg‐type inequalities for their spectral dispersions, and the quantization of the angular momentum modulus are introduced without using operators or commutation relations. The purpose is to focus the attention on angular momemtum as a very important practical concept of quantum physics, as well as on its specifically quantum‐theoretical aspects, right from the beginning of an introductory course. Since the heuristic arguments employed here closely parallel the rigorous derivations of a formal approach, the intuitive presentation does not contradict, but rather supports, the theoretical concepts to be introduced at a later stage.

ISSN:0002-9505    

DOI:10.1119/1.10118

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

The Stark effect of the plane rotator is a pedagogically appealing problem for undergraduate courses on quantum mechanics and, accordingly, has appeared in a number of textbooks as an application of bound‐state perturbation theory. Despite this fact and the apparent simplicity of the problem, all of the published accounts of it are erroneous in that they employ nondegenerate perturbation theory and present incorrect expressions for the perturbed eigenvalues and eigenstates. In this paper the problem is given a new treatment, based upon a simple analysis of symmetry features and a careful application of degenerate perturbation theory. The major shortcomings of previous discussions are pointed out and correct expressions are derived, to second order, for the perturbed state vectors and energy levels. The lifting of the twofold degeneracy of themth unperturbed excitation energy in the 2mth order of perturbation theory is demonstrated. Finally, a comparison of the correct perturbation‐theoretic results with the exact solution of the problem shows the two to be in identical correspondence.

ISSN:0002-9505    

DOI:10.1119/1.10119

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

We point out that a convenient way to construct wave packets is to superimpose bound‐state eigenfunctions. The resulting packets can be used to study spreading, scattering, and reflection as well as features unique to bound‐state phenomena. The infinite square well and the infinite square well with a δ‐function barrier are illustrated.

ISSN:0002-9505    

DOI:10.1119/1.10120

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

We have generated a number of phase‐space diagrams for several physically significant differential equations, including those describing the motion of a driven, damped pendulum and a Josephson weak link. These phase‐space diagrams can lead to considerable insight into the complex behavior exhibited by these systems. A number of these phase‐space diagrams were generated with parameters that can be duplicated with suitable mechanical models, allowing them to be used in conjunction with such models for a detailed study of the behavior of the driven, damped pendulum and Josephson weak link.

ISSN:0002-9505    

DOI:10.1119/1.10121

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

The retarded interaction of two dipole oscillators is discussed using classical electromagnetic theory. We show how the oscillators causally exchange excitation, and how the back‐and‐forth signalling between the oscillators results in the familiar first‐order dispersion or dipole–dipole interaction. These results are directly analogous to recently reported work on the quantum‐mechanical radiative interaction of two atoms ’’sharing’’ a single excitation.

ISSN:0002-9505    

DOI:10.1119/1.10122

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

The thermodynamic behavior of the one‐dimensional Bose‐gas–attractive‐δ impurity system is studied in this paper. The system is shown to undergo the Bose–Einstein condensation and the cause of the phase transition is attributed to the bound state introduced by the impurity in the free‐particle energy spectrum. The condensed phase is composed of particles captured by the impurity, forming a drop of particles well localized in space. This gives to the Bose–Einstein condensation in this system the appearance of the ordinary vapor–liquid phase transition. The expression for the pressure is obtained and is plotted as a function of the temperature and the system length. The shapes of the isothermal curves reinforce the interpretation of a vapor–liquid transition. The evaluation of the heat capacity at constant length shows the existence of a finite discontinuity at the transition temperature.

ISSN:0002-9505    

DOI:10.1119/1.10123

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

There are many ways of demonstrating electric and magnetic fields for introductory physics students, but in most instances onlyqualitativefeatures of fields are treated. Sometimes, a student may be misled into believing that the electric field produced in a shallow electrolytic tank by two small electrodes is the same as the field produced by two equal and opposite charges (or by a bar magnet) in free space. In this paper we show how somequantitative, but purely geometrical, features of field lines can be used to distinguish between these two cases. Equations are derived for field lines and radii of curvature of field lines for several idealized cases. We show that the radius of curvature of a field line is a unique and distinguishing feature of each of the four charge configurations treated. These purely geometrical criteria are applied to two typical experimental field plots to characterize them and to show that experimental constraints introduce departures from theoretical models.

ISSN:0002-9505    

DOI:10.1119/1.10124

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

The Gelfand–Levitan formulation of the inverse problem is briefly reviewed and then used as a source of exactly solvable bound‐state models which are suitable for examples in quantum mechanics courses. The case of one bound state is discussed in detail with emphasis on the role of the arbitrary normalization constant and its connection with physical parameters. An application to the deuteron is given. Possible pedagogical uses of these models are cited.

ISSN:0002-9505    

DOI:10.1119/1.10125

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

In order to spare the beginning student the task of extracting the meaning of a symbol from the context in which it is used, a scheme is suggested in which the letter–symbols of the Latin alphabet alone, together with superscript and subscript notation, are sufficient to provide a unique representation for almost any concept encountered in physics.

ISSN:0002-9505    

DOI:10.1119/1.10127

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP

摘要:

The angular momentum L of the electromagnetic field due to an electric point chargee, and a magnetic point charge (pole)g, is calculated by several methods to obtain J. J. Thomson’s result thatL=eg/c, and L is directed along the line joining the electric monopole to the magnetic monopole. The relation to Dirac’s monopoles is discussed, and particle size is considered.

ISSN:0002-9505    

DOI:10.1119/1.10310

出版商:American Association of Physics Teachers    

年代:1976

数据来源: AIP