NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (1), P. 79-94
ON THE DERIVATION OF THE SCHRÖDINGER EQUATION WITH POINT-LIKE NONLINEARITY
C. Cacciapuoti – Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy; claudio.cacciapuoti@uninsubria.it
In this report we discuss the problem of approximating nonlinear delta-interactions in dimensions one and three with regular, local or non-local nonlinearities. Concerning the one dimensional case, we discuss a recent result proved in [10], on the derivation of nonlinear delta-interactions as limit of scaled, local nonlinearities. For the three dimensional case, we consider an equation with scaled, non-local nonlinearity. We conjecture that such an equation approximates the nonlinear delta-interaction, and give an heuristic argument to support our conjecture.
Keywords: Nonlinear Schrödinger equation, nonlinear delta interactions, zero-range limit of concentrated nonlinearities.
PACS 02.30.Jr, 03.65.Db, 02.30.Rz
DOI 10.17586/2220-8054-2015-6-1-79-94
I love assembling useful information , this post has got me even more info! .
Do you have a spam issue on this website; I also am a blogger, and I was wanting to know your situation; many of us have created some nice methods and we are looking to trade strategies with other folks, be sure to shoot me an e-mail if interested.
Howdy! I know this is somewhat off topic but I was wondering which blog platform are you using for this site? I’m getting sick and tired of WordPress because I’ve had issues with hackers and I’m looking at options for another platform. I would be great if you could point me in the direction of a good platform.
I have been absent for a while, but now I remember why I used to love this web site. Thank you, I¦ll try and check back more frequently. How frequently you update your web site?
I enjoy your writing style genuinely loving this internet site.
Hi there just wanted to give you a quick heads up. The text in your content seem to be running off the screen in Opera. I’m not sure if this is a format issue or something to do with web browser compatibility but I thought I’d post to let you know. The style and design look great though! Hope you get the problem solved soon. Many thanks
Valuable information. Lucky me I found your website by accident, and I’m shocked why this accident did not happened earlier! I bookmarked it.
Attractive section of content. I just stumbled upon your weblog and in accession capital to assert that I acquire actually enjoyed account your blog posts. Any way I will be subscribing to your feeds and even I achievement you access consistently rapidly.