Dispersion of Klauder's temporally stable coherent states for the hydrogen atom

We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasi-classically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.Comment: 6 pages, 2 figure

Geometric phase effects for wavepacket revivals

The study of wavepacket revivals is extended to the case of Hamiltonians which are made time-dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase (Berry's phase) causes the revived packet to be displaced along the classical trajectory, by an amount equal to the classical geometric phase (Hannay's angle), in one degree of freedom. A physical example illustrating this effect in three degrees of freedom is mentioned.Comment: Revtex, 11 pages, no figures

Curvature in orbital dynamics

The physical basis,and the geometrical significance of the equation for the orbit of a particle moving under the action of external forces is exhibited by deriving this equation in a coordinate-independent representation in terms of the radius of curvature of the orbit. Although this formulation appeared in Newton's Principia, it has been ignored in contemporary classical mechanics textbooks. For small eccentricities, the orbit equation is used to obtain approximate solutions that illustrate the role of curvature. It is shown that this approach-leads to a simple graphical method for determining the orbits for central forces. This method is similar to one attributed to Newton, who applied it to a constant central force, and sent a diagram of the orbit to Hooke in 1679. The result is compared to. the corresponding orbit of a ball revolving inside an inverted cone which Hooke described in his response to Newton. (c) 2005 American Association of Physics Teachers

The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of Statistical Mechanics

In 1916 Einstein introduced the first rules for a quantum theory of electromagnetic radiation, and he applied them to a model of matter in thermal equilibrium with radiation to derive Planck's black-body formula. Einstein's treatment is extended here to time-dependent stochastic variables, which leads to a master equation for the probability distribution that describes the irreversible approach of Einstein's model towards thermal equilibrium, and elucidates aspects of the foundation of statistical mechanics. An analytic solution of this equation is obtained in the Fokker-Planck approximation which is in excellent agreement with numerical results. At equilibrium, it is shown that the probability distribution is proportional to the total number of microstates for a given configuration, in accordance with Boltzmann's fundamental postulate of equal a priori probabilities for these states. While the counting of these configurations depends on particle statistics- Boltzmann, Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined here by the dynamics which are embodied in the form of Einstein's quantum transition probabilities for the emission and absorption of radiation. In a special limit, it is shown that the photons in Einstein's model can act as a thermal bath for the evolution of the atoms towards the canonical equilibrium distribution of Gibbs. In this limit, the present model is mathematically equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which has been discussed recently by Ambegaokar and Clerk

States prepared by decay

We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.Comment: 22 pages, Latex2.09, 6 Postscript figures embedded using psfig, see also http://www.physics.helsinki.fi/~kasuomin/ To appear in a Special Issue of Journal of Modern Optics (1997

Observing the spin of a free electron

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions

First Simultaneous Optical and EUV Observations of the Quasi-Coherent Oscillations of SS Cygni

Using EUV photometry obtained with the Extreme Ultraviolet Explorer (EUVE) satellite and UBVR optical photometry obtained with the 2.7-m telescope at McDonald Observatory, we have detected quasi-coherent oscillations (so-called ``dwarf nova oscillations'') in the EUV and optical flux of the dwarf nova SS Cygni during its 1996 October outburst. There are two new results from these observations. First, we have for the first time observed ``frequency doubling:'' during the rising branch of the outburst, the period of the EUV oscillation was observed to jump from 6.59 s to 2.91 s. Second, we have for the first time observed quasi-coherent oscillations simultaneously in the optical and EUV. We find that the period and phase of the oscillations are the same in the two wavebands, finally confirming the long-held assumption that the periods of the optical and EUV/soft X-ray oscillations of dwarf novae are equal. The UBV oscillations can be simply the Rayleigh-Jeans tail of the EUV oscillations if the boundary layer temperature kT_bb <~ 15 eV and hence the luminosity L_bb >~ 1.2e34 (d/75 pc)^2 erg/s (comparable to that of the accretion disk). Otherwise, the lack of a phase delay between the EUV and optical oscillations requires that the optical reprocessing site lies within the inner third of the accretion disk. This is strikingly different from other cataclysmic variables, where much or all of the disk contributes to the optical oscillations.Comment: 16 pages including 3 tables and 4 encapsulated postscript figures; LaTeX format, uses aastex.cls; accepted on 2001 August 2 for publication in The Astrophysical Journa

Determination of masses and other properties of extra-solar planetary systems with more than one planet

Recent analysis of the Doppler shift oscillations of the light from extra-solar planetary systems indicate that some of these systems have more than one large planet. In this case it has been shown that the masses of these planets can be determined without the familiar ambiguity due to the unknown inclination angle of the plane of the orbit of the central star provided, however, that its mass is known. A method is presented here which determines also a lower limit to the mass of this star from these observations. As an illustration, our method is applied to the Keck and Lick data for GJ876.Comment: 10 pages, 17 figures. Accepted for publication in Astrophysical Journa