کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1855194 | 1645435 | 2010 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The string of variable density: Perturbative and non-perturbative results The string of variable density: Perturbative and non-perturbative results](/preview/png/1855194.png)
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeneities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions.
Journal: Annals of Physics - Volume 325, Issue 12, December 2010, Pages 2679–2696