摘要:

The supersymmetry‐inspired WKB approximation (SWKB) in quantum mechanics is discussed in detail. The SWKB method can be easily applied to any potential whose ground‐state wave function is known. It yields eigenvalues that are exact for large quantum numbersn(as any WKB approximation should in the classical limit). Furthermore, for the important special case of ‘‘shape‐invariant’’ potentials, the SWKB approach gives the exact analytic expressions for the entire bound‐state spectra. A study of some nonshape‐invariant, but solvable, potentials suggests that shape invariance is not only sufficient but perhaps even necessary for the SWKB approximation to be exact. A comparison of the WKB and SWKB predictions for the bound‐state spectra of a number of potentials reveals that in many cases the SWKB approach does better than the usual WKB approximation.

ISSN:0002-9505    

DOI:10.1119/1.16840

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

In his letter of 6 January 1679/80 Hooke wrote to Newton ‘‘in truth I agree with You that the Explicating the Curve in which a body Descending to the Center of the Earth, would circumgyrate were a Speculation of noe Use yet’’ [TheCorrespondenceofIsaacNewton, edited by H. W. Turnbull (Cambridge U.P., Cambridge, 1960), Vol. 2, p. 309]. In these words, Hooke referred to a hypothetical problem which he was discussing in a correspondence with Newton. The problem was that of determining the orbit of a body moving inside a narrow cut made centrally across the Earth. This was perhaps the very first inverse central force problem to be attacked by Newton. Newton seems to have used his instantaneous impulse technique to provide a drawing of a solution that was almost exact. This paper explores this fascinating early solution of an inverse central force problem.

ISSN:0002-9505    

DOI:10.1119/1.16751

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

It is shown that quick and elegant solutions of many problems in plane motion of a rigid body may be obtained by taking moments around the instantaneous center of rotation.

ISSN:0002-9505    

DOI:10.1119/1.16752

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

The Dalgarno–Lewis technique [A. Dalgarno and J. T. Lewis, ‘‘The exact calculation of long‐range forces between atoms by perturbation theory,’’ Proc. R. Soc. London Ser. A233, 70–74 (1955)] provides an elegant method to obtain exact results for various orders in perturbation theory, while avoiding the infinite sums which arise in each order. In the present paper this technique, which perhaps has not been exploited as much as it could be, is first reviewed with attention to some of its not‐so‐straightforward details, and then six examples of the method are given using three different one‐dimensional bases.

ISSN:0002-9505    

DOI:10.1119/1.16753

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

The analysis of the importance of the amplitude and the phase of Fourier transform has been carried out by means of combining these functions between two images and observing the reconstructed image after a second transform. This processing has been studied by taking into account several possibilities, especially for very structurally different images. It is proved that the phase carries the most relevant information, but when common images are combined with images constituted by strongly marked geometric forms it is not so evident and the amplitude could play a more important role.

ISSN:0002-9505    

DOI:10.1119/1.16754

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

The formulas for the relativistic transformation of velocity, acceleration, and higher derivatives are obtained in a simple way using the concept of the differential of a function. LetF0be a Lorentz transformation. Given the transformationFn, this paper describes a process by which one can construct the transformationFn+1. Starting with the given Lorentz transformationF0, this process yields a sequence of transformationsF1,F2,F3,... . Although the Lorentz transformationF0is linear,Fn, for alln>0, are nonlinear. The differentials of these nonlinear transformations give the correct transformation formulas for velocity, acceleration, and all higher‐order derivatives.

ISSN:0002-9505    

DOI:10.1119/1.16755

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

摘要:

In the present paper, the Gordon and Zarmi model is applied for the conversion of solar energy into wind energy, in such a way that simple calculations lead to a universal result: The upper bound for the conversion efficiency of solar energy into wind energy equals 8.3%.

ISSN:0002-9505    

DOI:10.1119/1.16756

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16757

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16758

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16760

出版商:American Association of Physics Teachers    

年代:1991

数据来源: AIP