Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.Comment: 13 page

A progressive diagonalization scheme for the Rabi Hamiltonian

A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and full matrix diagonalization.Comment: 8pages, 1 figure, LaTeX. Accepted for publication in J. Phys. B: At. Mol. Opt. Phy

Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials.Comment: 26 pages, no figure, reduced secs. 4 and 5, final version to appear in JP

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.Comment: 25 pages, 1 figur

Two Electrons in a Quantum Dot: A Unified Approach

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.Comment: 14 page

A new approach to the exact solutions of the effective mass Schrodinger equation

Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrodinger equation is also solved for the Morse potential transforming to the constant mass Schr\"{o}dinger equation for a potential. One can also get solution of the effective mass Schrodinger equation starting from the constant mass Schrodinger equation.Comment: 14 page

Expedition 302 summary

The first scientific drilling expedition to the central Arctic Ocean was completed in September 2004. Integrated Ocean Drilling Program Expedition 302, Arctic Coring Expedition (ACEX), recovered sediment cores to 428 meters below seafloor (mbsf) in water depths of ~1300 m, 250 km from the North Pole.Expedition 302's destination was the Lomonosov Ridge, hypothesized to be a sliver of continental crust that broke away from the Eurasian plate at ~56 Ma. As the ridge moved northward and subsided, marine sedimentation occurred and continues to the present, resulting in what was anticipated from seismic data to be a continuous paleoceanographic record. The elevation of the ridge above the surrounding abyssal plains (~3 km) ensured that sediments atop the ridge were free of turbidites. The primary scientific objective of Expedition 302 was to continuously recover this sediment record and to sample the underlying sedimentary bedrock by drilling and coring from a stationary drillship.The biggest challenge during Expedition 302 was maintaining the drillship's location while drilling and coring in 2–4 m thick sea ice that moved at speeds approaching 0.5 kt. Sea-ice cover over the Lomonosov Ridge moves with one of the two major Arctic sea-ice circulation systems, the Transpolar Drift, and responds locally to wind, tides, and currents. Until now, the high Arctic Ocean Basin, known as "mare incognitum" within the scientific community, had never before been deeply cored because of these challenging sea-ice conditions.Initial results reveal that biogenic carbonate is present only in the Holocene–Pleistocene interval. The upper 198 mbsf represents a relatively high sedimentation rate record of the past 18 m.y. and is composed of sediment with ice-rafted debris and dropstones, suggesting that ice-covered conditions extended at least this far back in time. Details of the ice type (e.g., iceberg versus sea ice), timing, and characteristics (e.g., perennial versus seasonal) await further study. A hiatus occurs at 193.13 mbsf, spanning a 25 m.y. interval from the early Miocene to the middle Eocene between ~18 Ma and 43 Ma. The sediment record during the middle Eocene is of dark, organic-rich biosiliceous composition. Isolated pebbles, interpreted as ice-rafted dropstones, are present down to 239 mbsf, well into this middle Eocene interval. Around the lower/middle Eocene boundary an abundance of Azolla spp. occurs, suggesting that a fresh and/or low-salinity surface water setting dominated the region during this time period. Although predrilling predictions based on geophysical data had placed the base of the sediment column at 50 Ma, drilling revealed that the uppermost Paleocene to lowermost Eocene boundary interval, well known as the Paleocene/Eocene Thermal Maximum (PETM), was recovered. During the PETM, the temperature of the Arctic Ocean surface waters exceeded 20°C.Drilling during Expedition 302 also penetrated into the underlying sedimentary bedrock, revealing a shallow-water depositional environment of Late Cretaceous age

Methods

Information assembled in this chapter will help the reader understand the basis for the preliminary conclusions of the Expedition 302 Scientists and will also enable the interested investigator to select samples for further analyses. This information concerns offshore and onshore operations and analyses described in the "Sites M0001–M0004" chapter. Methods used by various investigators for shore-based analyses of Expedition 302 samples will be described in the individual contributions published in the Expedition Research Results and in various professional journals