摘要:

We describe the details involved in presenting the time development of one-dimensional quantum-mechanical systems in the form of computer-generated motion pictures intended for pedagogic purposes. Concentrating on reflection-transmission phenomena, we formulate the problem in terms of a Gaussian wave packet impinging on a square well or barrier and being reflected and transmitted. The wave equation is solved numerically by methods discussed in detail and photographs of the wave packet vs position at a variety of times and for a range of projectile energies are given.

ISSN:0002-9505    

DOI:10.1119/1.1973991

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

Although a basic assumption in Chandrasekhar's theory of the dynamical friction acting on a star in a cluster has been regarded as disqualifying his theory for adaptation to an electron in a plasma, it is shown here that a new adaptation, with recognition of a contrast between the effects of other electrons and of ions, leads to a good formula for the friction. That is, it leads to a formula agreeing with one which Sitenko and Chien deduced from the Fokker-Planck equation. Disagreements with certain other Fokker-Planck theories have been traced to definite errors in these theories. Finally, Chandrasekhar's assumption that the friction exerted gravitationally on the star is the same as if only one other star acted on this one at any one time has been re-examined; and relatively simple reasons have been found for the validity of the electrostatic equivalent of his assumption, even though great numbers of electrons and ions act on an electron in a plasma at any one time.

ISSN:0002-9505    

DOI:10.1119/1.1973994

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

An experiment has been designed for undergraduate educational use. Deuterons from a 150-keV Cockcroft-Walton accelerator bombarded a thin6Litarget, producing6Li(d,p1)7Li*,6Li(d,p0)7Li,6Li(d,α)4He,6Li(d,n1)7Be*, and6Li(d,n0)7Be. Equipment utilized is of the type which is either in or available to many departments of modest size. Properly used, such equipment constitutes an educational tool, teaching current research methods at reasonable cost. To this end, protons, alphas, neutrons, and gammas from the above reactions have been examined in a manner designed to be most instructive. Alpha and proton energies have been measured as a function of laboratory angle, and compared with kinematic calculations. Absolute differential cross sections have been derived from these data. A spectrum has also been made of the gammas from6Li(d,n1)7Be*and6Li(d,p1)7Li*. Gamma-proton and gamma-neutron coincidences measurements have been used to verify energy-level assignments. Angular correlation of the observed alphas has also been studied to show conservation of momentum and the effects of center-of-mass motion.

ISSN:0002-9505    

DOI:10.1119/1.1973998

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

The problem of the darkness of the night sky, or Olbers' paradox, as currently referred to, received but sporadic attention on the part of astronomers and cosmologists until the formulation of the steady-state theory in 1948. The frequent references by the proponents of that theory to Olbers' views on the paradox are, however, at a baffling variance with the contents of Olbers' original paper published in 1826. This situation is a telling illustration of the scientists' often unscientific handling of the data of scientific history.

ISSN:0002-9505    

DOI:10.1119/1.1974001

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

In quantum mechanics the linear harmonic oscillator representatives of the canonical observablesqandpare certain well-known infinite square matrices,qmnandpmn, with denumerable sets of rows and columns. It is pedagogically useful to investigate various problems which arise when one considers the finite matricesQmnandPmnwhich result whenqmnandpmnare truncated after theNthrow and column, whereN( 2≥2) is some preassigned positive integer. So that the enquiry may be more instructive, it begins with an abstract formulation of the problem of the “truncated harmonic oscillator.” Formally, the latter has the usual HamiltonianH = 12( Q2+P2 ), butQandPare not canonical—their commutator[Q,P]now differing fromiby a certain projection operator. The spectrum ofHand the (finite) basis{ |n〉} generated byHare found by standard methods, though there are now some complications which are absent from the theory of the linear harmonic oscillator. The diagonalization ofQandPpresents no difficulties if full use is made of the classical theory of Hermite polynomials. The spectrum ofQis the set ofNzeroshsof theNthHermite polynomial. Although the wavefunctions〈 Q′|n〉 are therefore functions of thediscretevariablehs, one can formally contemplate them as functions of a continuous real variableh; and some curious intimations of Schrödinger representation appear. The analog of a component of orbital angular momentum is considered, and its spectrum obtained. Finally, the asymptotic limitN → ∞is briefly discussed, in order thus explicitly to dispel the impression that this limit might somehow represent the “usual” linear harmonic oscillator.

ISSN:0002-9505    

DOI:10.1119/1.1974004

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

A graphical model of Keplerian planetary motion is used to deduce the inverse-square law of force. Invariant velocity components are utilized that reflect the geometric properties of the elliptic planetary orbit and the geometric characteristics of the vector quantities, force, and linear momentum.

ISSN:0002-9505    

DOI:10.1119/1.1974007

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

Experiments suggest that the effect observed with Manchester's microwave Doppler-shift apparatus may be interpreted as a counting of interference fringes. This fringe-counting frequency is the same as that obtained from the Doppler-shift lower beat frequency, and does not invalidate the use of the apparatus for velocity measurements. In reflection from a moving mirror, and other Doppler-effect experiments where interference is possible, fringe counting may be regarded as an aspect of the Doppler effect; the connection between the fringe-counting frequency and the Doppler-frequency shift is provided by the fact that a linearly time-varying phase is equivalent to a constant-frequency shift.

ISSN:0002-9505    

DOI:10.1119/1.1974010

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

Electrostatic experiments can be performed successfully even in humid climates if precautions against surface moisture are taken. A generator capable of delivering charge at a fixed, reproducible potential is described. A commercial electrometer is used as a high-impedance voltmeter to permit various experiments involving static charges on capacitors. The electrometer permits the construction of a simple probe for exploring both the magnitude and the direction of an electric field. The transition to circuit electricity is made by experiments employing capacitor discharge.

ISSN:0002-9505    

DOI:10.1119/1.1974013

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

The phenomenon of ambipolar diffusion is one of the most fundamental in the gaseous plasmas normally encountered in glow discharges and low-pressure arcs. In spite of its apparent simplicity, its manifestations outside of a few “classical” situations can be relatively complicated, and make it a difficult matter to treat with a sufficient degree of generality. The extensions to the case with an external electric field, to that of a noncylindrical positive column, to that of a plasma with a magnetic field are considered. A possible clue to the case of a weakly ionized, weakly magnetized plasma of noncylindrical form is suggested.

ISSN:0002-9505    

DOI:10.1119/1.1974015

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP

摘要:

A derivation of Liouville's equation is given using the formalism employed by Hopf (1952) and Edwards (1964) in their derivation of the equations governing, respectively, the characteristic-density functional and probability-density functional associated with turbulent fluids.

ISSN:0002-9505    

DOI:10.1119/1.1974017

出版商:American Association of Physics Teachers    

年代:1967

数据来源: AIP