The method of continued fractions for multichannel scattering
✍ Scribed by A.J. Makowski; A. Raczyński; G. Staszewska
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 288 KB
- Volume
- 114
- Category
- Article
- ISSN
- 0009-2614
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This note jollows the work of Lagrange and Euler and gives the essential steps for reaching a solution of the Boole and the Riccati equations with the help of continued fractions. The resulta are compared with the series solutions (which may be recognized in closed form for simple caaea) obtained by
Analytical possibilities of the continued fraction method are demonstrated by solving two problems connected with a description of slow electron resonance scattering by positive molecular ions. Using the rotation adiabatic approximation, exact solutions of the multiquantum vibrational transition pro
Let F F be the family of continued fractions K a r1 , where a s yg , a s g x , ps2, 3, . . . , with 0 F g F 1, g fixed, and x F 1, p s py 1 p p p p p 2, 3, . . . . In this work, we derive upper bounds on the errors in the convergents of Ž . K a r1 that are uniform for F F, and optimal in the sense