کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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978575 | 933293 | 2009 | 13 صفحه PDF | دانلود رایگان |
We analyze the extension of the well known relation between Brownian motion and the Schrödinger equation to the family of the Lévy processes. We consider a Lévy–Schrödinger equation where the usual kinetic energy operator–the Laplacian–is generalized by means of a selfadjoint, pseudodifferential operator whose symbol is the logarithmic characteristic of an infinitely divisible law. The Lévy–Khintchin formula shows then how to write down this operator in an integro-differential form. When the underlying Lévy process is stable we recover as a particular case the fractional Schrödinger equation. A few examples are finally given and we find that there are physically relevant models–such as a form of the relativistic Schrödinger equation–that are in the domain of the non stable Lévy–Schrödinger equations.
Journal: Physica A: Statistical Mechanics and its Applications - Volume 388, Issue 6, 15 March 2009, Pages 824–836