摘要:

According to Hartree's self-consistent-field (SCF) model of the atom, the motion of each electron in the effective field of theN-1 others is governed by a one-particle Schrödinger equation. Self-consistency of the electronic charge distribution with its own electrostatic field leads to a set of coupled integrodifferential equations (Hartree equations) forNone-particle wavefunctions (atomic orbitals). The Hartree equations were subsequently shown to be precisely the conditions for optimization of an approximate wavefunction consisting of a product of atomic orbitals. An improved formalism, due to Slater and to Fock, represents the atomic wavefunction by a determinant built of atomic spin-orbitals and is thereby consistent with the Pauli principle. Application of the variational principle to a Slater determinant leads to a set ofNcoupled equations (Hartree-Fock equations), quite similar to Hartree's equations but containing, in addition, exchange interactions—an effect having no classical analog. The error inherent in the Hartree-Fock method, known as electron correlation, arises from smoothing-out of interelectronic repulsive interactions into effective Coulomb and exchange potentials. It accounts for roughly a 1% error in the total energy but is magnified in energy differences, which are more directly related to experimental quantities. A significant improvement in computational facility is achieved if the orbital functions are expanded in terms of a finite set of basis functions. The integrodifferential equations are thereby transformed into algebraic equations (Roothaan's equations) for the expansion coefficients. The analytic approach makes it possible to apply the self-consistent-field method to molecular systems. To date, SCF calculations have been carried out, in some form, for all the atoms in the periodic table and for a growing list of diatomic and polyatomic molecules.

ISSN:0002-9505    

DOI:10.1119/1.1971665

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

A calculation of selected energy levels in a Yukawa potential utilizing the Bohr theory yields results which are in good agreement with those given by more difficult methods. A new result obtained is an expression for the number of bound states.

ISSN:0002-9505    

DOI:10.1119/1.1971669

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

The path described by a rolling truncated sphere is shown to be an equiangular spiral. An undergraduate laboratory experiment is described in which this motion is studied.

ISSN:0002-9505    

DOI:10.1119/1.1971675

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

An historical review of Lorentz-covariant scalar theories of gravitation is presented. Included are the theory of Poincaré, its presentation by Kottler, and its modification by Whitrow and Morduch; the first theory of Nordström, its modified form due to Bergmann, the modifications due to Whitrow and Morduch, and the field-theoretic approach of Thirring; the second theory of Nordström; and the theory of Kustaanheimo. The extent to which these theories can be said to be in accord with the experimental evidence concerning red shift, advance of the perihelion of Mercury, and deflection of light rays is discussed. It is found that except for red shift, there is, at best, poor agreement and, at worst, disagreement.

ISSN:0002-9505    

DOI:10.1119/1.1971681

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

Undergraduate use of a large computer operated in the time-sharing mode is described. Data obtained in three nuclear physics experiments which were done in the laboratory part of the second-year physics course were analyzed with the aid of programs written for this computer.

ISSN:0002-9505    

DOI:10.1119/1.1971686

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

By working directly from Newtonian equations of motion and representing accelerationẍas[(x,H), H], families of Hamiltonians may be constructed which are functions of the energy and which, while describing the same classical motions, are not connected by canonical transformations. One dimensional examples are given, and the formal rules of quantization executed whenHis(energy)12to show that the quantum motion does not come out right. The reason is that the commutation rule(x,p) = iħdoes not have universal standing; quantum theory in employing this rule is apparently requiring not merely thatHbe a generator of motion, but also that it be a very particular one, viz., the energy when the system is conservative.

ISSN:0002-9505    

DOI:10.1119/1.1971690

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

The American Association of Physics Teachers annually cites some of its members for distinguished service to the teaching of physics. Three citations, prepared by Vincent E. Parker, Chairman of the Committee on Awards, were presented by President Edward U. Condon at the Annual Meeting of the Association on 30 January 1965.

ISSN:0002-9505    

DOI:10.1119/1.1971695

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

For experiments in forced linear oscillation, a square wave is integrated to a triangular wave, and that is shaped by a pair of diodes to approximate a sine wave. The response of a galvanometer driven by the shaped wave matches quite closely the response calculated for a pure sinusoidal forcing function over the frequency range of interest here, from 0.5 to 2 times the resonant frequency. One advantage of the circuit is that the student observes the phase lag quite directly.

ISSN:0002-9505    

DOI:10.1119/1.1971698

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

It is shown that a bar of diamagnetic material suspended freely in a uniform magnetic field aligns itself with the long axis parallel to the field, just as does a bar with positive susceptibility.

ISSN:0002-9505    

DOI:10.1119/1.1971703

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP

摘要:

The chief properties of separable, nonlocal potentials in quantum theory are pointed out and exemplified by solving the Schrödinger equation for the one-dimensional motion of a particle in an attractive separable square well.

ISSN:0002-9505    

DOI:10.1119/1.1971708

出版商:American Association of Physics Teachers    

年代:1965

数据来源: AIP