ISSN:0002-9505    

DOI:10.1119/1.18995

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.19064

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

We describe an apparatus that will sense the vibration of a wineglass through the jitter induced on a laser beam reflected from the glass wall. A positive feedback system provides a high level sound-wave-train that maintains the vibration of the glass, while a light-emitting diode lighting panel, also deriving its signal from the feedback system, allows the motion of the glass to be clearly observed in a user-controllable way. The positive feedback signal, along with observations from some additional experiments, can be used to highlight some of the nonlinear aspects of the resonance. Although the apparatus is primarily intended as a demonstration exhibit, we have found it useful also as a physics teaching aid.

ISSN:0002-9505    

DOI:10.1119/1.19031

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

We present an example of how two nonidentical oscillators can synchronize due to dynamical nonlinear interactions. This highlights a classic distinction with coupled linear oscillators, a difference which is important to the functioning of several systems in physics and biology. We illustrate the phenomenon using an electronic circuit appropriate for an advanced undergraduate physics lab.

ISSN:0002-9505    

DOI:10.1119/1.18984

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

The specific features of scattering of the Gaussian wave packet by the simplest of all reflectionless potentials, the Sech-squared well, are considered. The results of numerical computation show that a wave packet that has passed through this potential overtakes a free wave packet and is both higher and narrower than a free wave packet; in other words, the scattered wave packet accelerates inside the well and preserves its shape better. Comparisons with scattering by the square well and by a series of reflectionless potentials are also presented. Possible applications of the Sech-squared as well as other reflectionless potentials are discussed.

ISSN:0002-9505    

DOI:10.1119/1.18985

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

A simple example of the mass–energy relation is given by using electromagnetic calculations for a classical hydrogen atom, a point mass electron moving under the Coulomb force in a uniform circular orbit around a heavy point mass proton when the radiation-reaction self-force is neglected. The system mass is determined by calculating the ratio of the total external force to the system acceleration in the limit of small acceleration, and is shown to be equal toc−2times the total system energy including the particle rest-mass energies, the particle kinetic energies, and the electrostatic potential energy. From the equivalence principle, the external forces can be regarded either as accelerating the atom relative to an inertial frame or else as supporting the atom in a gravitational field. The calculations are carried out for two different models. In the first case, the atom is regarded as accelerated by a frictionless surface which applies forces to both the electron and the proton. In the second case, the atom is accelerated by a single external force applied to the proton, and the electron orbit is displaced relative to the proton. In both cases the accelerating forces are constant forces and there are no external forces stabilizing the system.

ISSN:0002-9505    

DOI:10.1119/1.18986

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated numerically for the case of a spherical well potential and analytically for this and other soluble potentials. Provided that the potential is of a finite range and that the binding is weak, the theorem gives a useful approximation for the short-distance behavior of the scattering wave functions. The connection between bound and scattering-state perturbation theory is established in this limit.

ISSN:0002-9505    

DOI:10.1119/1.18987

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

We illustrate the description of correlated subsystems by studying the simple two-body hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in the framework of the density matrix formalism, describes correlations in the electron–proton motion.

ISSN:0002-9505    

DOI:10.1119/1.18977

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

A profound analogy between the Landau damping of plasma waves and the resonant mechanism of wave generation on a water surface by wind is discussed. A new simple derivation of the former effect is presented which explicitly demonstrates the essential role of the integrals of motion (the vorticity for an inviscid fluid, and the particle distribution function for a collisionless plasma) in these phenomena.

ISSN:0002-9505    

DOI:10.1119/1.18978

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP

摘要:

Chaotic dynamics of the two-body conservative system, which consists of a particle of massmbouncing elastically on a horizontal plate of massMsupported by an elastic spring, is investigated. The system integrates the properties of coupled oscillators with those of the bouncing-ball and impact oscillator problems. Results obtained by varying the mass ratioM/mand the spring constantkin numerical computations are presented in the form of time-dependent diagrams and discrete maps. The rich variety of resulting chaotic behavior includes strange attractors with fractal structure, resonant islands, crisis, and intermittency route to chaos. The system has a remarkable didactic value as an example of chaotic behavior in simple systems close to everyday experience. The integrable limitM=0is appropriate for introducing the phase portraits and discussing the interrelationship between the shape of the potential energy curves and the resulting oscillatory motion.

ISSN:0002-9505    

DOI:10.1119/1.18979

出版商:American Association of Physics Teachers    

年代:1998

数据来源: AIP