Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 218, Issue 13, Pages 7308-7321Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2012.01.009
Keywords
Analytic solution; Generalized Schrodinger equation; Darboux transformation; Supersymmetry; Hopf-Cole transformation; Transformed potential; Hamiltonian
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Funding
- Ministry of Education of China [0213-812002, 20100041120037]
- Natural Sciences Foundation of China [11026165, 50909017]
- Fundamental Research Funds for the Central Universities [JGK101677, DUT11SX03]
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In this paper, analytically investigated is a generalized one-dimensional time-dependent Schrodinger equation. Using Darboux transformation operator technique, we construct the first-order Darboux transformation and the real-valued condition of transformed potential for the generalized Schrodinger 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 Schrodinger equation. (C) 2012 Elsevier Inc. All rights reserved.
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