کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4631057 | 1340615 | 2012 | 14 صفحه PDF | دانلود رایگان |

In this paper, analytically investigated is a generalized one-dimensional time-dependent Schrödinger equation. Using Darboux transformation operator technique, we construct the first-order Darboux transformation and the real-valued condition of transformed potential for the generalized Schrödinger equation. To prove the equivalence of the supersymmetry formalism and the Darboux transformation, we investigate the relationship among first-order Darboux transformation, supersymmetry and factorization of the corresponding effective mass Hamiltonian. Furthermore, the nth-order Darboux transformations are constructed by means of different method. Finally, by using Darboux transformation, some analytical solutions are generated in a recursive manner for some examples of the Schrödinger equation.
Journal: Applied Mathematics and Computation - Volume 218, Issue 13, 1 March 2012, Pages 7308–7321