کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4632085 | 1340635 | 2010 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Numerical solution of the one-dimensional time-independent Schrödinger's equation by recursive evaluation of derivatives
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We develop a simple numerical method for solving the one-dimensional time-independent Schrödinger's equation. Our method computes the desired solutions as Taylor series expansions of arbitrarily large orders. Instead of using approximations such as difference quotients for the derivatives needed in the Taylor series expansions, we use recursive formulas obtained using the governing differential equation itself to calculate exact derivatives. Since our approach does not use difference formulas or symbolic manipulation, it requires much less computational effort when compared to the techniques previously reported in the literature. We illustrate the effectiveness of our method by obtaining numerical solutions of the one-dimensional harmonic oscillator, the hydrogen atom, and the one-dimensional double-well anharmonic oscillator.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 215, Issue 12, 15 February 2010, Pages 4400-4405
Journal: Applied Mathematics and Computation - Volume 215, Issue 12, 15 February 2010, Pages 4400-4405
نویسندگان
Asai Asaithambi,