Exact and Approximate Solutions of Spectral Problems for the Schrödinger Operator on (−∞, ∞) with Polynomial Potential
New exact representations for the solutions of numerous one-dimensional spectral problems for the Schrödinger operator with polynomial potential are obtained by using a technique based on the functional-discrete (FD) method. In the cases where the ordinary FD-method is divergent, we propose to use its modification, which proves to be quite efficient. The obtained theoretical results are illustrated by numerical examples.
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- 8.V. L. Makarov, “FD-method in spectral problems for the Schrödinger operator with polynomial potential on (−∞, +∞),” Dop. Nats. Akad. Nauk Ukr., No. 11, 5–11 (2015).Google Scholar
- 9.V. L. Makarov, “On a functional-difference method of any order of accuracy for the solution of the Sturm–Liouville problem with piecewise smooth coefficients,” Dokl. Akad. Nauk SSSR, 1 (320), 34–39 (1991).Google Scholar
- 10.V. L. Makarov, “FD-method—exponential rate of convergence,” Zh. Obchysl.. Prykl. Mat., No. 82, 69–74 (1997).Google Scholar
- 12.V. L. Makarov and N. M. Romanyuk, “New properties of the FD-method in its application to Sturm–Liouville problems,” Dop. Nats. Akad. Nauk Ukr., No. 2, 26–31 (2014).Google Scholar
- 13.F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (editors), NIST Digital Library of Mathematical Functions, Cambridge Univ. Press, New York (2010).Google Scholar