Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator

Distribution of Virus-Infected Bacteria in the Western Equatorial Pacific.

v. ill. 23 cm.QuarterlyViruses are generally considered an important agent of bacterial loss in diverse marine environments. However, the impact of viruses on bacteria is unknown in the western equatorial Pacific, where surface waters are warm and phytoplankton biomass is low (i.e., oligotrophic). Further, little is known about their importance in the mesopelagial, where bacteria and heterotrophic nanoflagellates are known to be metabolically active. To elucidate the ecological characteristics of viruses in the western equatorial Pacific, abundances of bacteria and viruses were measured, along with frequencies of visibly infected cells (FVIC) and frequencies of dividing cells (FDC) in epipelagic and mesopelagic samples at three stations near the equator from August to September 2002. Measurements of Secchi depth (20 m) and chlorophyll a concentrations (0.07– 0.4 mg chl a liter_1) indicated that the study area was oligotrophic during the investigation. FVIC ranged from 0.4% to 1.8% and 0.5% to 1.8% in the epipelagic and mesopelagic zones, respectively. Virally induced bacterial mortality was inferred to range from 4.5% to 20.8% in the epipelagic zone, suggesting that viruses contribute substantially to bacterial mortality in oligotrophic seawaters. In addition, these values were similar to those estimated for the mesopelagic zone (5.0%–21.2%). Overall, viruses appear to be an important factor in the loss of bacterial production in both oligotrophic epipelagic and mesopelagic zones in the study area

The Wave Function and the Minimum Uncertainty Function of the Time Dependent Harmonic Oscillator(New Developments in Statistical Physics Similarities in Diversities,YITP Workshop)

この論文は国立情報学研究所の電子図書館事業により電子化されました。The time dependent harmonic oscillator is solved explicitly for quantum mechanics by the operator method with an auxiliary condition as the classical solution. Two classical invariant quantities which determine whether or not the system is bound are derived by the classical equation of motion. We obtain the invariant operator from one classical invariant quantity. Its eigenfunction is related to the solution of Schrodinger equation of the system and its eigenvalue is related to another classical quantity. The wave function is evaluated exactly by the eigenfunction of the invariant operator but it is not the eigenfunction of the Hamiltonian of the system. The uncertainty which calculates with the wave function is not a minimum one. We will confirm that the function which holds minimum uncertainty is a eigenfunction of the Hamiltonian

The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation

Coherent states and uncertainty relations for the damped harmonic oscillator with time-dependent frequency

Starting with evaluations of propagator and wave function for the damped harmonic oscillator with time-dependent frequency, exact coherent states are constructed. These coherent states satisfy the properties which coherent states should generally have