Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures. Sent to Ann. Physics (2004

Quantum mechanical sum rules for two model systems

Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems, the infinite well and the single delta-function potential. These cases illustrate the different ways in which such sum rules can be realized, and the varying mathematical techniques by which they can be confirmed. Using the same methods, we also evaluate the second-order energy shifts arising from the introduction of a constant external field, namely the Stark effect.Comment: 23 pages, no figures, to appear in Am. J. Phy

Eigenvalue bounds for polynomial central potentials in d dimensions

If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian H = - Delta + f(r), where f(r)=sum_{i = 1}^{k}a_ir^{q_i}, 2\leq q_i < q_{i+1}, a_i \geq 0$, then the eigenvalues E = E_{n\ell}^{(d)}(\lambda) are given approximately by the semi-classical expression E = \min_{r > 0}[\frac{1}{r^2} + \sum_{i = 1}^{k}a_i(P_ir)^{q_i}]. It is proved that this formula yields a lower bound if P_i = P_{n\ell}^{(d)}(q_1), an upper bound if$P_i = P_{n\ell}^{(d)}(q_k) and a general approximation formula if P_i = P_{n\ell}^{(d)}(q_i). For the quantum anharmonic oscillator f(r)=r^2+\lambda r^{2m},m=2,3,... in d dimension, for example, E = E_{n\ell}^{(d)}(\lambda) is determined by the algebraic expression \lambda={1\over \beta}({2\alpha(m-1)\over mE-\delta})^m({4\alpha \over (mE-\delta)}-{E\over (m-1)}) where \delta={\sqrt{E^2m^2-4\alpha(m^2-1)}} and \alpha, \beta are constants. An improved lower bound to the lowest eigenvalue in each angular-momentum subspace is also provided. A comparison with the recent results of Bhattacharya et al (Phys. Lett. A, 244 (1998) 9) and Dasgupta et al (J. Phys. A: Math. Theor., 40 (2007) 773) is discussed.Comment: 13 pages, no figure

The Stark effect in linear potentials

We examine the Stark effect (the second-order shift in the energy spectrum due to an external constant force) for two 1-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions give closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.Comment: 15 pages. To appear in Eur. J. Phys. Needs Institute of Physics (iopart) style file

Complete genome sequence of the Medicago microsymbiont Ensifer (Sinorhizobium) medicae strain WSM419

Ensifer (Sinorhizobium) medicae is an effective nitrogen fixing microsymbiont of a diverse range of annual Medicago (medic) species. Strain WSM419 is an aerobic, motile, non-spore forming, Gram-negative rod isolated from a M. murex root nodule collected in Sardinia, Italy in 1981. WSM419 was manufactured commercially in Australia as an inoculant for annual medics during 1985 to 1993 due to its nitrogen fixation, saprophytic competence and acid tolerance properties. Here we describe the basic features of this organism, together with the complete genome sequence, and annotation. This is the first report of a complete genome se-quence for a microsymbiont of the group of annual medic species adapted to acid soils. We reveal that its genome size is 6,817,576 bp encoding 6,518 protein-coding genes and 81 RNA only encoding genes. The genome contains a chromosome of size 3,781,904 bp and 3 plasmids of size 1,570,951 bp, 1,245,408 bp and 219,313 bp. The smallest plasmid is a fea-ture unique to this medic microsymbiont

Ca and Mg isotope fractionation during the stoichiometric dissolution of dolomite at temperatures from 51 to 126 degrees C and 5 bars CO2 pressure

Natural polycrystalline hydrothermal Sainte Colombe dolomite was dissolved in stirred titanium closed system reactors in aqueous 0.1 mol/kg NaCl solutions at 51, 75, 121, and 126 °C and a pressure of 5 bars CO2. In total, 52, 27, 16, and 12%, respectively, of the dolomite placed in the reactors dissolved into the fluid phase during these experiments. Each experiment lasted from 12 to 47 days and the fluid phase in each evolved towards, but did not exceed, ordered dolomite equilibrium at a pH of 5.9 ± 0.3. All aqueous reactive fluids were undersaturated with respect to all potential secondary phases including calcite and magnesite. The reactive fluid compositions at the end of the experiments had a molar Ca/Mg ratio equal to that of the dissolving dolomite, and the dolomite recovered after the experiments contained only pure dolomite as verified by scanning electron microscopy. The Ca and Mg isotopic ratios of the reactive fluids remained within uncertainty equal to that of the dissolving dolomite in the experiments performed at 51 and 75 °C. In contrast, the Ca isotopic composition of the reactive fluid in the experiment performed at 121 and 126 °C was significantly greater such that Δ44/42Casolid-fluid = − 0.6 ± 0.1‰, whereas that of Mg was within uncertainty equal to that of the dissolving mineral. The equilibrium fractionation factors for both divalent cations favor the incorporation of isotopically light metals into the dolomite structure. Our results at 121 and 126 °C, therefore, are consistent with the one-way transfer of Mg from dolomite to the fluid but the two-way transfer of Ca from and to dolomite as equilibrium is approached during its stoichiometric dissolution. The lack of Mg returning to the dolomite structure at these conditions is attributed to the slow dehydration kinetics of aqueous Mg. As more than 12% of the dolomite dissolved during the 121 and 126 °C closed system experiments, our observations indicate a significant change in the Ca isotopic signature of the dolomite during its stoichiometric dissolution. Moreover, as there is no visual evidence for dolomite recrystallization during this experiment, it seems likely that the resetting of Ca isotopic signatures of carbonate minerals can be readily overlooked in the interpretation of natural systems

Trace Element Patterns in Shells of Mussels (Bivalvia) Allow to Distinguish between Fresh- and Brackish-Water Coastal Environments of the Subarctic and Boreal Zone

The accumulation of trace metals in the shells of bivalves allows quantitative assessments of environmental pollution and helps to reconstruct paleo aquatic environments. However, the understanding on how marine and freshwater mollusks control the level of trace elements in their shells remains very limited. Here, we compared the trace element composition of marine and freshwater bivalves from boreal and subarctic habitats, using examples of widely distributed species of marine (Mytilus edulis, M. trossulus) and freshwater (Anodonta anatina, Unio sp., Beringiana beringiana) mussels. Sizable differences in several trace element concentrations were detected between different species, depending on their environmental niches. A multiparametric statistical treatment of the shell’s elemental composition allowed to distinguish the impact of external factors (water and sediment chemical composition) from active metabolic (biological) control. In particular, the obtained results demonstrated that Ba:Ca and Pb:Ca ratios in mussels’ shells are closely related to the primary productivity of aquatic ecosystems. The Mn:Ca ratio allowed to constrain the environmental conditions of mussels’ species depending on the trophic state of inhabited waterbody. Overall, the marine mussels exhibited stronger biological control of trace element accumulation, whereas trace element pattern in shells of freshwater mussels was chiefly controlled by environmental factors. The obtained results might help to use the trace element composition of bivalves in distinguishing marine and freshwater habitats of mollusks in paleo environments