Highly Excited States of a Hydrogen Atom in a Strong Magnetic Field

Classical trajectories and semiclassical energy eigenvalues are calculated for an atomic electron in a high Rydberg state in an external magnetic field. With the use of perturbation theory, a classical trajectory is described as a Kepler ellipse with orbital parameters evolving slowly with time. As they evolve, the ellipse rocks, tilts, and flips in space, but the length of its major axis remains approximately constant. Exact numerical calculations verify that perturbation theory is quite accurate for the cases considered (principal quantum number ≃ 30, magnetic field ≲ 6 T). Action variables are calculated from perturbation theory and from exact trajectories, and semiclassical eigenvalues are obtained by quantization of action. Excellent agreement is found with observations

Semiclassical Calculation of Quantum-Mechanical Wave Functions for a Two-Dimensional Scattering System

The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for two‐dimensional scattering from a Morse potential. The characteristic function S and the density Jacobian J are computed in order to obtain the primitive wave function. The incident part shows distorted plane‐wave behavior and the scattered part shows radially outgoing behavior. A uniform approximation gives a wave function that is well‐behaved near the caustic

Trajectories of an Atomic Electron in a Magnetic Field

Classical trajectories of an atomic electron in a magnetic field are calculated for various values of the field strength B. Qualitative properties of these trajectories are examined. With use of a scaling law, it is shown that the equations of motion can be written in a form such that they depend upon only one parameter, which may be regarded as a reduced angular momentum (proportional to LzB13). For small values of this parameter there is an elliptical regime in which the trajectory may be regarded as a Kepler ellipse with orbital parameters that evolve slowly in time. For large values of the parameter there is a helical regime in which the electron circles rapidly around a magnetic field line and bounces slowly back and forth along the field. Between these two regimes there is an irregular regime, with chaotic orbits and a transition regime in which the trajectories can be described in oblate spheroidal coordinates. Bound states persist even at energies above the escape energy, provided that the angular momentum (or field strength) is sufficiently large. With use of action-variable quantization, some formulas for semiclassical energy eigenvalues are given for regimes where the trajectories are regular

Bound State Semiclassical Wave Functions

The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for a two‐dimensional bound state system. We investigate in detail an eigenstate of a coupled anharmonic oscillator system. The primitive semiclassical wave function is obtained from the characteristic function S and the density function J. Each of these functions consists of four branches corresponding to the four possible directions of motion of the classical trajectory through any point. The interference from the four branches determines the basic structure of the wave function. A uniform approximation gives a wave function which is well behaved along each caustic and which is in good agreement with the fully quantal wave function

Semiclassical Theory of Inelastic Collisions I. Classical Picture and Semiclassical

This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, iℏddtdi(t)=Σjhij(t)dj(t), which describe the time dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared

Geometry and Topology of Escape. II. Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each end point of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an “Epistrophe Start Rule:” a new epistrophe is spawned Δ=D+1 role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ=D+1Δ=D+1 iterates after the segment to which it converges, where D role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eD is the minimum delay time of the complex

Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem

We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. We prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ for various families of graphs. In particular, we show that if the maximum degree of a graph $G$ on $n$ vertices is $n-O(1)$ or $n-\Omega(n)$, then $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ is at most $O(n)$

Atomic Electrons in Strong Magnetic Fields: Transition from Elliptical to Helical Behavior.

The behavior of an atomic electron in a static magnetic field strong enough to correspond to the transition regime is examined. The field strength is characterized by the parameter L^, the effective component of angular momentum. A Floquet-Mathieu analysis shows that the bifurcation of classical trajectories into elliptical and helical families is related to the 2:1 resonance which occurs at L^=L^T. Quantum mechanics gives an avoided crossing at L^T; we examine the nature of the wave functions as L^ passes through the resonance. Semiclassical calculations accurately reproduce the quantum eigenvalues and produce trajectories which underlie the quantum wave functions. The avoided crossing is expressed in semiclassical terms as a switch between elliptical and helical families. The bifurcation of the classical motion means that, at the primitive semiclassical level, some states may be missed and others may be generated in both elliptical and helical representations

The World Trade Center Disaster and the Health of Workers: Five-Year Assessment of a Unique Medical Screening Program

BACKGROUND: Approximately 40,000 rescue and recovery workers were exposed to caustic dust and toxic pollutants following the 11 September 2001 attacks on the World Trade Center (WTC). These workers included traditional first responders, such as firefighters and police, and a diverse population of construction, utility, and public sector workers. METHODS: To characterize WTC-related health effects, the WTC Worker and Volunteer Medical Screening Program was established. This multicenter clinical program provides free standardized examinations to responders. Examinations include medical, mental health, and exposure assessment questionnaires; physical examinations; spirometry; and chest X rays. RESULTS: Of 9,442 responders examined between July 2002 and April 2004, 69% reported new or worsened respiratory symptoms while performing WTC work. Symptoms persisted to the time of examination in 59% of these workers. Among those who had been asymptomatic before September 11, 61% developed respiratory symptoms while performing WTC work. Twenty-eight percent had abnormal spirometry; forced vital capacity (FVC) was low in 21%; and obstruction was present in 5%. Among nonsmokers, 27% had abnormal spirometry compared with 13% in the general U.S. population. Prevalence of low FVC among nonsmokers was 5-fold greater than in the U.S. population (20% vs. 4%). Respiratory symptoms and spirometry abnormalities were significantly associated with early arrival at the site. CONCLUSION: WTC responders had exposure-related increases in respiratory symptoms and pulmonary function test abnormalities that persisted up to 2.5 years after the attacks. Long-term medical monitoring is required to track persistence of these abnormalities and identify late effects, including possible malignancies. Lessons learned should guide future responses to civil disasters

Growth requirements of Rhizoctonia repens M 32

Rhizoctonia repens M 32, a mycorrhizal isolate from Orchis militaris requires both a carbohydrate (glucose or sucrose) and an amino acid (aspartic acid, glycine, serine, or glutamic acid) for growth. The fungus does not require an exogenous supply of vitamins in vitro. © 1975 Dr. W. Junk bv - Publishers