کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10735941 | 1045079 | 2005 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We consider nonlinear Schrödinger equations which have been proposed as fundamental equations of nonlinear quantum theories. The equations are singular in that the wave function Ï appears in the denominator of rational expressions. To avoid the problem of zeros of Ï it is natural to make the ansatz Ï = eν. This ansatz, however, conflicts with the-physically motivated-requirement that the solutions Ï be square integrable. We show that this conflict can be resolved by considering an unusual function space whose definition involves the derivative âν of ν. This function space turns out to be dense subset of L2 and the equations can be solved in the L2-sense (as desired) by first solving an evolutionary system for âν and then transforming back to Ï.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Reports on Mathematical Physics - Volume 56, Issue 2, October 2005, Pages 291-310
Journal: Reports on Mathematical Physics - Volume 56, Issue 2, October 2005, Pages 291-310
نویسندگان
Holger Teismann,