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Ukrainian Mathematical Journal

, Volume 70, Issue 1, pp 84–100 | Cite as

Exact and Approximate Solutions of Spectral Problems for the Schrödinger Operator on (−∞, ∞) with Polynomial Potential

  • V. L. Makarov
Article
  • 19 Downloads

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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. L. Makarov
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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