The attractive nonlinear delta-function potential
| Autor: | M. I. Molina, C. A. Bustamante |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Physics
Mathematical analysis Physics - Physics Education Plane wave FOS: Physical sciences General Physics and Astronomy Dirac delta function State (functional analysis) Nonlinear system symbols.namesake Physics - General Physics General Physics (physics.gen-ph) Physics Education (physics.ed-ph) Bound state symbols Exponent Delta potential Sign (mathematics) |
| Zdroj: | AMERICAN JOURNAL OF PHYSICS Artículos CONICYT CONICYT Chile instacron:CONICYT |
| ISSN: | 1943-2909 0002-9505 |
| DOI: | 10.1119/1.1417529 |
| Popis: | We solve the continuous one-dimensional Schr\"{o}dinger equation for the case of an inverted {\em nonlinear} delta-function potential located at the origin, obtaining the bound state in closed form as a function of the nonlinear exponent. The bound state probability profile decays exponentially away from the origin, with a profile width that increases monotonically with the nonlinear exponent, becoming an almost completely extended state when this approaches two. At an exponent value of two, the bound state suffers a discontinuous change to a delta-like profile. Further increase of the exponent increases again the width of the probability profile, although the bound state is proven to be stable only for exponents below two. The transmission of plane waves across the nonlinear delta potential increases monotonically with the nonlinearity exponent and is insensitive to the sign of its opacity. Comment: submitted to Am. J. of Phys., sixteen pages, three figures |
| Databáze: | OpenAIRE |
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