Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with asymptotically periodic potentials

We consider one-dimensional Fokker-Planck and Schr\"odinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be applicable to such asymptotically periodic cases. Using this method, we study the low-energy behavior of the Green function.Comment: author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretica

The More She Longs for Home, the Farther Away it Appears: A Paradox of Nostalgia in a Fulani Immigrant Girl’s Life

Nostalgia, which is derived from the Greek words nos (returning home) and algia (pain), refers to longing for the loss of the familiar (Kaplan, 1987). The loss of our connection to the familiar is a painful experience as such loss is connected to a fundamental loss, the loss of ourselves. By losing a connection to familiar people, objects, and places that continue to remain the same from the past to the future, we also lose the continuity within ourselves. And this discontinuity of our past, present, and future selves creates anxiety within us (Milligan, 2003). The painful experience that accompanies the loss of the familiar and the severe longing for the lost was originally viewed as a type of depression, which required psychiatric treatment. However, increasing mobility and changes in modern society have made nostalgia a more typical experience for many. Nostalgia is a relevant experience particularly for immigrants who live away from their homeland

Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function

SL(3,C) structure of one-dimensional Schr\"odinger equation

We present a new formalism for describing solutions of the one-dimensional stationary Schr\"odinger equation in terms of the Lie group SL(3,C) and its Lie algebra. In this formalism, we obtain a universal expression for the Green function which can be used in any representation of SL(3,C) and also expressions for various quantities involving products of Green functions. Specifically, we introduce an infinite-dimensional representation of SL(3,C) that provides a natural description of multiple scattering of waves. Using this particular representation, we can derive formulas which are useful for the analysis of the Green function.Comment: 32 pages, 15 figure