摘要:

We argue for greater use of the no-dispersion approximation in introductory courses on quantum mechanics for the following two basic reasons: (i) the approximation yields in many situations a simple serniclassical picture of the time development of localized wavepackets; (ii) it makes explicit the fundamental importance of phase relations in the quantum model.

ISSN:0002-9505    

DOI:10.1119/1.1986802

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

Minimal equipment is used in a sophomore laboratory experiment demonstrating Faraday's Law. A complicated mathematical expression for the induced EMF is solved with an electronic desk calculator or computer for comparison with experimental results. Data are given for a typical experiment.

ISSN:0002-9505    

DOI:10.1119/1.1986803

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

We describe how to perform signal averaging using a multichannel analyzer without internal modification. It thus becomes possible to average signals with the aid of “borrowed” equipment. Required equipment, in addition to a multichannel analyzer, consists of approximately $100 worth of transistor circuitry and a voltage to frequency converter.

ISSN:0002-9505    

DOI:10.1119/1.1986804

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

Satyendranath Bose's recognition of the fact that the photons in a cavity radiator are indistinguishable led him to a derivation of the Planck law free from any assumptions of classical electrodynamics. His result, published in 1924, was a significant vindication of the photon concept that Einstein had championed since 1905. It also laid the foundations of quantum statistics, as was freely acknowledged by Einstein and Dirac, among others. Various aspects of Bose's career, including his apparent failure to understand the full implications of his work, may be of interest both to physicists and historians of science.

ISSN:0002-9505    

DOI:10.1119/1.1986805

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

In this paper we investigate the advantages of using the product-integral calculus rather than the usual successive approximation perturbative expansion in three branches of quantum physics. The mathematics of the calculus is fully developed, and its superiority over the perturbative expansion is explored in specific examples from physics. All of time-dependent perturbation theory in quantum mechanics can be written in terms of the calculus, as well as the most general solution for the density operator in quantum statistical mechanics.

ISSN:0002-9505    

DOI:10.1119/1.1986806

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

Considerable insight into elementary atomic theory is generated by constraining the atomic Hamiltonian of atoms with few electrons by demanding that the electrons be as far apart as possible. This and other simplifying assumptions allow us to separate Schrödinger's equation by reducing the problem to a geometrical analog. The analogous problem is to locate dots symmetrically on the surfaces of concentric spheres consistently with the Pauli principle and with the dots as far apart as possible. The resulting equations permit calculation of effective nuclear charges which are used to find the total energy of the system from a hydrogenlike energy formula. The energies so determined are compared to experimental values, and derived screening terms are compared to those of Slater's rules. Our energies are consistently lower than experimental values. Several unanswered questions opened by this technique are proposed as possible further research on a level suitable for an undergraduate paper.

ISSN:0002-9505    

DOI:10.1119/1.1986807

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The Maxwell-Boltzmann Distribution (MBD) for a classical ideal gas is obtained as the mean over phase space of the number of momentum components less than some value p, without making any assumptions beyond those implicit in the microcanonical ensemble. The variance of the fluctuations of actual distributions of the momentum around the average given by the MBD is shown to go to zero asN−1,whereNis the number of particles. This proof of the MBD has the advantage over the usual type of proof in that it does not employ a subdivision of phase space into cells, a trick which gives rise to certain difficulties discussed in the introduction. Moreover, it is more complete in that the problem of the fluctuations is treated at an elementary level.

ISSN:0002-9505    

DOI:10.1119/1.1986808

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The application of finite-difference equations in the solution of repetitive multiloop resistive circuits in one-and two-dimensional configurations is discussed in both finite and infinite cases. The technique of solution involves only ordinary algebra and trigonometry. Yet one can see the emergence of simple orthogonal functions and the finite-difference approximations of the Cauchy-Riemann equations and Laplace's equation. Boundary-value problems can be presented and understood at a simple level of physics and mathematics. Such repetitive structures can serve as discrete approximative models for various physical properties of continuous media. The implications for the teaching of boundary-value problems in electricity are brought out.

ISSN:0002-9505    

DOI:10.1119/1.1986809

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

Two methods for obtaining the ladder spectrum characteristic of the simple harmonic oscillator are widely used in elementary quantum mechanics. In the first method, that of series solution, quantization is shown to follow from the requirement that the wave function be normalizable. In the second, it is common to derive quantisation in an operator formalism based on factorization of the wave equation. In this latter method the role of normalizability is not customarily discussed. We show explicitly that the same boundary condition implicit in the operator manipulations leads to quantization in both methods.

ISSN:0002-9505    

DOI:10.1119/1.1986810

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

This essay is motivated to add a useful note to the contemporary literature of ideal gases. For brevity, a new description is given for a special class of ideal quantum gases (the “qsuper ideal gases”) which are characterized here by two compact equations of state. Within such a framework all fundamental properties of these gases are readily expressed in terms of two constants known as the state indices. In order to test our results of deduction, six typical examples are given with comparable numerical values. While all the examples must otherwise have resort to statistical calculations, our evaluation for them turns out to be straightforward as well as heuristic.

ISSN:0002-9505    

DOI:10.1119/1.1986811

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP