摘要:

When a system of particles in a bound state is placed in an external field the quantum state of the system depends on the manner in which the field is produced. The two limiting cases of interest are the adiabatic and impulse limits. Since the system does not approach a stationary state in either limit, in general, it is necessary to consider solutions of the time dependent Schrödinger equation. An example of this approach is provided by the problem of a harmonic oscillator in a uniform, time varying electric field for which an exact solution is easy to obtain using the Magnus expansion for the evolution operator. This operator contains the position and momentum in a particularly simple way that allows it to be interpreted in terms of position and momentum shifts produced by the field. The wavefunction of the oscillator is obtained in the adiabatic and impulse limits assuming the field to be switched on in an exponential fashion. Results obtained for these two limiting cases are then shown to be independent of the manner in which the field reaches its final steady value.

ISSN:0002-9505    

DOI:10.1119/1.1986457

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

This is a tutorial article concerned with problems related to dates and, geometrical alignments determined from astronomical considerations. The mathematical problems often arise in connection with attempts to specifiy days of the year in the past or in connection with ancient edifices. In this way the solutions are of interest to anthropologists, archeologists, art historians, folklorists, historians, and astronomy enthusiasts. While the methods of solution presented are general, specific problems are also employed for illustrative purposes. Some problems involve the famous ancient edifices of Abu Simbel, Cheops' Pyramid, and Stonehenge, and bright celestial objects such as the Sun, Sirius, and the Pleiades. Solutions depend on a knowledge of spherical trigonometry and basic astronomy, and often involve the phenomenon of the precession of the Earth's spin axis. Effects of precession are described geometrically and algebraically.

ISSN:0002-9505    

DOI:10.1119/1.1986458

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

A discussion of linear collisions between two or three objects is presented. This presentation has proved to be very effective in a junior-level course in analytical mechanics. The theoretical discussion uses a geometrical approach that treats elastic and inelastic collisions from a unified point of view. This approach gives the student a physical "feeling" for the effect of imposing varying amounts of inelasticity on a two- or three-body collision. Momentum and energy constraints are used to delimit the region, in the space of final velocities, that contains all possible solutions. Experiments with a linear air track demonstrate how changing the interparticle forces produces widely differing final states og motion.

ISSN:0002-9505    

DOI:10.1119/1.1986459

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

This paper presents a way to use a computer in the teaching of introductory, stationary state, Schrödinger quantum mechanics. The method is based upon an easily explained computer method; a 20-line program in BASIC is presented to implement the strategy. Not only is this numerical technique completely general for all one-dimensional and all spherically symmetric, three-dimensional problems, but also it allows the student to be introduced to topics of interest such as asymptotic solutions. Several examples of the use of the computer technique are presented.

ISSN:0002-9505    

DOI:10.1119/1.1986460

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The problem of energy propagation through a one-dimensional open-ended finite chain is critically re-examined. Free end boundary conditions are imposed and quantum-field-theory operators, consistent with these boundary conditions, are derived for both the local and total energy current operators, avoiding the shortcomings of previous work reported on the subject. The formal treatment is illustrated through an example, and a comparison with results obtained with cyclic boundary conditions is given.

ISSN:0002-9505    

DOI:10.1119/1.1986461

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The transfer-matrix method is used to derive the characteristic equation for electron energy eigenvalues in a generalized infinite one-dimensional binary alloy. The alloy is divided into unit cells and subcells so that the method used is independent of the shape of the potential barriers. Application of the technique to a type-AB one-dimensional alloy represented by an infinite chain of two kinds of square potential barriers gives the energy eigenvalue equation for this case explicitly and for the first time. The formalism is also shown to give the Kronig-Penney result for a chain of identical square potentials.

ISSN:0002-9505    

DOI:10.1119/1.1986462

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The techniques of the 3nj invariants are applied to the finite molecular point groups in the classification of states and interaction operators and the evaluation of matrix elements. The hydrogen spin-rotation ofNH3is worked out in detail as an example.

ISSN:0002-9505    

DOI:10.1119/1.1986463

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

A laboratory is described that provides the student with a transitional experience between the more structured laboratories in introductory courses and the open-ended individual special problems. Vacuum ultraviolet spectroscopy has been chosen as the area of major emphasis as it provides an excellent vehicle for the student to learn a number of valuable experimental techniques. Experiments are outlined that use vacuum systems, radiation sources, dispersion, and detection systems to provide challenging laboratory experiences.

ISSN:0002-9505    

DOI:10.1119/1.1986464

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

The form of the equations of motion for a mechanical system subjected to nonholonomic constraints is discussed. A modified form of Gauss's principle of least constraint is used to derive the equations of motion for systems with nonlinear, nonholonomic constraints. Other derivations of these same equations of motion are discussed.

ISSN:0002-9505    

DOI:10.1119/1.1986465

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP

摘要:

Through the use of an example, it is indicated how the subject of variable mass systems may be introduced to even beginning students.

ISSN:0002-9505    

DOI:10.1119/1.1986466

出版商:American Association of Physics Teachers    

年代:1972

数据来源: AIP