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Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. (Phys. Lett. A, 124, 233 (1987). doi:10.1016/03759601(87)90627-X0) is reproduced to verify the method and results. A novel feature is the determination of the spectra of asymmetric hybrid linear and quadratic potentials. As in previous work, the singular perturbations are modeled by delta functions. Key words: green functions, confining potentials, singular perturbation, 1D solvable potentials, energy spectra. Motives par l'interet recent pour les potentiels quantiques de confinement, surtout en ce qui a trait a la spectroscopie de Stark de nouveaux puits quantiques, nous examinons plusieurs oscillateurs unidimensionnels singuliers. Nous appliquons une fonction de Green, passons en revue la construction des resolvantes necessaires et de nouvelles sont introduites. De plus, un travail anterieur sur le modele de l'oscillateur harmonique singulier tel qu'introduit par Avakian et al. (Phys. Lett. A, 124, 233 (1987). doi:10.1016/0375-9601(87)90627-X0) est reproduit afin de verifier la methode et les resultats. Une nouvelle caracteristique qui apparait ici est la determination des spectres des potentiels lineaire hybride asymetrique et quadratique. Comme dans les travaux precedents, les perturbations singulieres sont modelisees par des fonctions delta. [Traduit par la Redaction] Mots-cles : fonctions de Green, potentiels de confinement, perturbation singuliere, potentiels unidimensionnels resolubles, spectres d'energie. PACS Nos.: 02.30.Gp, 02.30.Hq, 02.30.Sa, 02.30.Tb, 03.65.-w, 03.65.Db, 03.65.Ge., 1. Introduction The bound state spectra in confining potentials, especially of linear and quadratic form, has been a concern in quark confinement, for example, for some time [1]. The effect [...]

We propose an approximate scaling property of the classical partition function of a two-dimenisional one-component plasma in a high magnetic field based on the molecular dynamics simulations of dubey and Gumbs [ABSTRACT FROM AUTHOR]

This paper develops a tectono-stratigraphic model for the evolution and drowning of Early Jurassic carbonate platforms. The model arises from outcrop analysis and Sr isotope dating of successions exposed in the Betic Cordillera in southeastern Spain. Here, an extensive Early Jurassic (Sinemurian) carbonate platform developed on the rifted Tethyan margin of the Iberian Plate. The platform was dissected by extensional faults in early jamesoni times (ca. 191 Ma) and again in late ibex times (ca.188 Ma) during the Pliensbachian stage. Extensional faults and fault block rotation are shown to control the formation of three sequence boundaries that divide the platform stratigraphy (the Gavilan Formation) into three depositional sequences. The last sequence boundary marks localised drowning of the platform and deposition of the deeper water Zegri Formation, whereas adjacent platforms remain exposed or continue as the site of shallow-marine sediment accumulation. This study is based on mapping, facies analysis and dating of platform carbonates exposed in three tectonic units within the zone: Gabar, Ponce and Canteras. Facies analysis leads to the recognition of facies associations deposited in carbonate ramp environments and adjacent to synsedimentary, marine, fault scarps. Sr isotope dating enables us to correlate platform-top carbonates from the different tectonic units at a precision equivalent to ammonite zones. A sequence stratigraphic analysis of sections from the three tectonic units is carried out using the facies models together with the Sr isotope dates. This analysis indicates a clear tectonic control on the development of the stratigraphy: depositional sequences vary in thickness, have wedge-shaped geometries and vary in facies, internal geometries and systems tracts from one tectonic unit to another. Criteria characterising depositional sequences and sequence boundaries from the Gabar and Ponce units are used to establish a tectono-stratigraphic model for carbonate platform depositional sequences and sequence boundaries in maritime rifts, which can be applied to other less well-exposed or subsurface successions from other sedimentary basins. Onlapping transgressive and progradational highstand systems tracts are recognised on dip slope ramps. Falling stage and lowstand systems tracts are developed as thick breccia units in hangingwall areas adjacent to extensional faults. Sequence boundaries vary in character, amplitude and/or duration of sea-level fall and persistence across the area. Some boundaries coalesce onto the Canteras unit, which remained as a relatively positive area throughout the early Pliensbachian (Carixian). The carbonate platform on the Ponce tectonic unit drowned in the latest Carixian ( davoei biozone). However, the adjacent tectonic units remained emergent and developed a long-lived sequence boundary, indicating tectonic subsidence as the major cause for platform drowning. The stratigraphic evolution of this area on the rifted southern Iberian margin indicates that a widespread restricted shallow-water carbonate platform environment accumulating peritidal carbonates evolved with faulting to a more open-marine setting. Sr dating indicates that this transition took place around the Sinemurian–Pliesbachian boundary and it was driven by local fault-related subsidence together with likely post-faulting regional subsidence. [ABSTRACT FROM AUTHOR]

Shows that for the hydrogenlike atom, with central potential, partial differential equations exist for the Slater sum and for its s-wave component. Construction of Slater sum for several illustrative central field problems; Description of the three-dimensional isotropic oscillator.

In one dimension, the Slater sum S(x, β), which is the diagonal element of the canonical density matrix, satisfies a known partial differential equation characterised by a one-body potential V(x). Here, for the case of a sech2 x potential in one dimension, it is stressed that S(x, β) is explicitly related to the limit S0(β) as V(x) → 0 and to V(x) itself. This is the same input information as in the Thomas-Fermi result. The relevance to density functional theory is emphasised. [ABSTRACT FROM AUTHOR]

The connection between the Schro¨dinger and confluent hypergeometric equations is discussed. It is shown that the factorization of the confluent hypergeometric equation gives a unifying powerful algebraic tool in order to study some quantum mechanical eigenvalue problems. That description includes the linear and N-dimensional harmonic oscillators, as well as the Coulomb and Morse potentials. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]