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

Double and triple summation expressions obtained using perturbation theory

Using standard perturbation theory, simple new double and triple summation expressions are obtained

Barium isotope (re-)equilibration in the barite-fluid system and its implications for marine barite archives

Variations in the Ba isotopic composition of seawater are largely driven by the extent of barite precipitation in the marine photic zone and replenishment of Ba by upwelling and/or continental inputs. Pelagic barites offer a robust tool for tracing sources and sinks of Ba in the (paleo)ocean as they record these isotopic variations. Knowledge of the Ba isotope fractionation between barite and ambient waters is therefore imperative. Here, the Ba isotope fractionation between barite and Ba2+ (aq) under equilibrium conditions has been estimated by the three-isotope method with a 135Ba-enriched reactive fluid. The estimated Ba isotope fractionation was Δ137/134BaBarite-Ba2+ = −0.07 ± 0.08‰. Textural observations of barite crystals recovered up to 756 days of reaction reveal smoothing of solid surfaces but also typical dissolution features such as development of pits and cracks. Thus, dissolution/re-precipitation is likely the mechanism controlling the observed isotope exchange that is facilitated by the further development of porosity in the crystals. Additionally, the isotope exchange in the experimental runs fits a second-order law yielding a surface normalized isotope exchange rate of ∼2.8 × 10−10 mol/m2/s. This exchange rate could theoretically result in complete isotope exchange between pelagic barite with a typical edge size of 1 μm and ambient seawater or pore fluid within years, altering the barite's Ba isotopic composition during settling towards the seafloor and/or after deposition in marine sediments. Although there is considerable uncertainty in extrapolating experimental results to natural conditions and longer time scales, the rapid rates of exchange observed experimentally over short timescales suggest that isotope exchange in pelagic barite should be considered during interpretation of the Ba isotope composition as a paleoarchive.</p

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