تقرير
Milne's Equation revisited: Exact Asymptotic Solutions
| العنوان: | Milne's Equation revisited: Exact Asymptotic Solutions |
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| المؤلفون: | Shu, D., Simbotin, I., Côté, R. |
| سنة النشر: | 2016 |
| المجموعة: | Physics (Other) |
| مصطلحات موضوعية: | Physics - Atomic Physics |
| الوصف: | We present novel approaches for solving Milne's equation, which was introduced in 1930 as an efficient numerical scheme for the Schr\"odinger equation. Milne's equation appears in a wide class of physical problems, ranging from astrophysics and cosmology, to quantum mechanics and quantum optics. We show how a third order linear differential equation is equivalent to Milne's non-linear equation, and can be used to accurately calculate Milne's amplitude and phase functions. We also introduce optimization schemes to achieve a convenient, fast, and accurate computation of wave functions using an economical parametrization. These new optimization procedures answer the long standing question of finding non-oscillatory solutions of Milne's equation. We apply them to long-range potentials and find numerically exact asymptotic solutions. Comment: 5 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1612.07849 |
| رقم الأكسشن: | edsarx.1612.07849 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |