摘要:

An analysis of the collapse postulate for a two‐system situation is given. Asuperpositionof product wavefunctions is used to define a homogeneous ensemble and amixtureof product wavefunctions to define a heterogeneous ensemble. The expectation value of a product of operators is considered, such that the first has nonzero matrix elements only for states pertaining to system 1 and the second only for states of system 2. A condition is derived for the expectation values as averaged over the two ensembles to be identical, i.e., for the collapse postulate to be unnecessary. The result is applied to (i) the measurement problem, (ii) the design of a possible experiment to test for the validity of the collapse postulate, and (iii) to the Einstein–Podolsky–Rosen (EPR) example. In many cases the collapse postulate is not needed in the ensemble picture. When it is needed it is equivalent to a random phase assumption of a kind which is usually employed in statistical mechanics.

ISSN:0002-9505    

DOI:10.1119/1.15321

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The introduction to rolling friction is studied in relation to the height that a ball attains rolling up an inclined track after rolling down a given height along another inclined track opposite from the first. The expressions obtained for a ball rolling down a rectangular inclined track and along a horizontal track are applied to the study of the distance run along two opposed inclined tracks. Different procedures are proposed to determine the coefficient of rolling friction of the ball with the track. The values calculated from the experimental data suggest their dependence with the ball radius.

ISSN:0002-9505    

DOI:10.1119/1.15223

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Evidence is presented suggesting an ancient heliocentrist origin for geocentrist C. Ptolemy’s planetary orbit elements and the equant. Pliny’s data for Venus are shown to be inconsistent with geocentricity, and a heliocentric period‐relation is found to be the basis of Ptolemy’s previously unexplained and astonishingly accurate tables of the mean motion of Mars, the very planet whose orbit produced the equant. The admirable correctness of his adopted Mars elements is patently inconsistent with the ordmag 1° inaccuracy of Ptolemy’s geocentric model and of his alleged empirical production.

ISSN:0002-9505    

DOI:10.1119/1.15224

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Specific heat is one of the oldest techniques used in condensed matter physics. This paper reviews the contributions made through specific heat measurements to our understanding of lattice vibrations in solids, starting with the work of Petit and Dulong in 1819. Recently, specific heat measurements have revealed new information on the lattice vibrations in glasses, i.e., structurally disordered systems and certain highly disordered, yet crystalline, solids. These two classes of solids contain anomalous low energy excitations which completely mask the specific heat resulting from plane wave excitations at low temperatures. Measurements of thermal relaxations (time dependent specific heat) in these solids have also demonstrated the limits of the concept of temperature in these solids in the low temperature limit.

ISSN:0002-9505    

DOI:10.1119/1.15225

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

An expression for the longitudinal spherical aberration produced by a spherical refracting surface from parallel incident light in the fifth‐order approximation is derived. A simple experiment to measure the location of focal points formed by nonparaxial rays is also described. The results of the measurements are in good agreement with the theory.

ISSN:0002-9505    

DOI:10.1119/1.15195

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The three‐dimensional Coulomb–Kepler problem is shown to be equivalent to a pair of coupled two‐dimensional harmonic oscillators with the same angular momentum in classical mechanics by means of a Kustaanheimo–Stiefel transformation of coordinates and velocities. The constraint condition inherent in the transformation is shown to be related to the Runge–Lenz vector. The relationship between the action variables of the two systems is discussed. The equivalence is seen to result in the separability of the problem in parabolic coordinates.

ISSN:0002-9505    

DOI:10.1119/1.15196

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

A uniformly accelerated reference frameSis defined as a set of observers who remain at rest with respect to a given observer A who is accelerating at a constant rate with respect to the instantaneously comoving inertial frames. The one‐dimensional uniformly accelerated reference frameSis considered. The world lines of A and the other observers making upSare determined. Coordinates useful for describing events inSare carefully defined and the transformation equations between different sets of them are derived. The variation with position inSof the speed and frequency of light waves is determined. The motion of a free‐particle inSis determined. Various phenomena inS, ordinarily associated with general relativity, are considered, in particular the asymmetric aging of twins at rest at different positions and the existence of horizons.

ISSN:0002-9505    

DOI:10.1119/1.15197

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Quantum action‐angle variables are used to describe and analyze a number of familiar systems. For a given system, the quantum canonical transformation from the old coordinates, e.g., linear or polar, to the new coordinates, action‐angle variables, is found by generalizing the corresponding classical transformation using a method based upon the correspondence principle, the Hermiticity and canonical nature of the old coordinates, and the requirement that the Hamiltonian be independent of the quantum angle variable. The bound‐state energy levels and other important system properties follow immediately from the canonical transformation. Harmonic oscillators of various dimensions and the three‐dimensional angular momentum system are used as illustrations; these illustrations provide interesting alternatives to the usual quantum treatments.

ISSN:0002-9505    

DOI:10.1119/1.15198

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

If a narrow line stimulus on an opposite contrast background is observed with appropriately misfocused vision, the stimulus appears as a number of alternating bright and dark fringes. A numerical calculation of this effect was performed. As a result it was found that the banding phenomenon is a Fresnel diffraction effect depending on the details of both the narrow line stimulus and the eye pupil.

ISSN:0002-9505    

DOI:10.1119/1.15175

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

It is shown that repeated differentiation, with respect to the perturbation parameter λ, of the equation 〈ψm(λ)‖H0+λV‖ψn(λ)〉 =En(λ)δmn, and methodical application of the closure relation ∑‖ψn〉〈ψn‖=1, provide a painless technique for deriving the energy corrections in the Rayleigh–Schrödinger perturbation theory. The procedure is compared with one based on solving the secular equationD(E)=0, whereDis the determinant whose elements are 〈ψi‖H0+V‖ψj〉−Eδij.

ISSN:0002-9505    

DOI:10.1119/1.15176

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP