Exact and Approximate Solutions of the Spectral Problems for the Differential Schrödinger Operator with Polynomial Potential in ℝK, K ≥ 2
- Authors: Makarov V.L.1
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Affiliations:
- Institute of Mathematics, Ukrainian National Academy of Sciences
- Issue: Vol 240, No 3 (2019)
- Pages: 289-322
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242745
- DOI: https://doi.org/10.1007/s10958-019-04354-2
- ID: 242745
Cite item
Abstract
We consider spectral problems for the Schrödinger operator with polynomial potentials in ℝK, K ≥ 2. By using a functional-discrete (FD-)method and the Maple computer algebra system, we determine a series of exact least eigenvalues for the potentials of special form. In the case where the traditional FD-method is divergent (the degree of the polynomial potential exceeds 2 at least in one variable), we propose a modification of the method, which proves to be quite efficient for the class of problems under consideration. The obtained theoretical results are illustrated by numerical examples.
About the authors
V. L. Makarov
Institute of Mathematics, Ukrainian National Academy of Sciences
Author for correspondence.
Email: makarov@imath.kiev.ua
Ukraine, Tereshchenkivs’ka Str., 3, Kyiv, 01004