WKB Approximation to the Power Wall

We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit $\alpha\to\infty$ would reproduce a perfectly reflecting boundary, but at present we concentrate on the cases $\alpha =1$ and 2, for which exact solutions in terms of well known functions are available for comparison. We classify the classical paths in this system by their qualitative nature and calculate the contributions of the various classes to the leading-order semiclassical approximation: For each classical path we find the action $S$, the amplitude function $A$ and the Laplacian of $A$. (The Laplacian is of interest because it gives an estimate of the error in the approximation and is needed for computing higher-order approximations.) The resulting semiclassical propagator can be used to rewrite the exact problem as a Volterra integral equation, whose formal solution by iteration (Neumann series) is a semiclassical, not perturbative, expansion. We thereby test, in the context of a concrete problem, the validity of the two technical hypotheses in a previous proof of the convergence of such a Neumann series in the more abstract setting of an arbitrary smooth potential. Not surprisingly, we find that the hypotheses are violated when caustics develop in the classical dynamics; this opens up the interesting future project of extending the methods to momentum space.Comment: 30 pages, 8 figures. Minor corrections in v.

A Tripartite Model of Group Identification: Theory and Measurement

Group identification is defined as member identification with an interacting group and is distinguished conceptually from social identity, cohesion, and common fate. Group identification is proposed to have three sources: cognitive (social categorization), affective (interpersonal attraction), and behavioral (interdependence). Inconsistent use of the term and problematic measurement mar existing literature on group identity and group identification. A new group identification scale, composed of three subscales that match the tripartite model for the cognitive, affective, and behavioral sources, is presented and its psychometric properties described.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Characterization of the thermal and photoinduced reactions of photochromic spiropyrans in aqueous solution

Six water-soluble spiropyran derivatives have been characterized with respect to the thermal and photoinduced reactions over a broad pH-interval. A comprehensive kinetic model was formulated including the spiro- and the merocyanine isomers, the respective protonated forms, and the hydrolysis products. The experimental studies on the hydrolysis reaction mechanism were supplemented by calculations using quantum mechanical (QM) models employing density functional theory. The results show that (1) the substitution pattern dramatically influences the pKa-values of the protonated forms as well as the rates of the thermal isomerization reactions, (2) water is the nucleophile in the hydrolysis reaction around neutral pH, (3) the phenolate oxygen of the merocyanine form plays a key role in the hydrolysis reaction. Hence, the nonprotonated merocyanine isomer is susceptible to hydrolysis, whereas the corresponding protonated form is stable toward hydrolytic degradation

Economics education and value change: The role of program-normative homogeneity and peer influence

In the light of corporate scandals and the recent financial crisis, there has been an increased interest in the impact of business education on the value orientations of graduates. Yet our understanding of how students' values change during their time at business school is limited. In this study,weinvestigate the effects of variations in the normative orientations of economics programs. We argue that interaction among economics students constitutes a key mechanism of value socialization, the effects of which are likely to vary across more-or-less normatively homogeneous economics programs. In normatively homogeneous programs, students are particularly likely to adopt economics values as a result of peer interaction. We specifically explore changes in power, hedonism, and self-direction values in a 2-year longitudinal study of economics students (N 5 197) in a normatively homogeneous and two normatively heterogeneous economics programs. As expected, for students in a normatively homogeneous economics program, interaction with peers was linked with an increase in power and hedonism values, and a decrease in self-direction values. Our findings highlight the interplay between program normative homogeneity and peer interaction as an important factor in value socialization during economics education and have important practical implications for business school leaders