2018
Том 70
№ 8

All Issues

Exact and approximate solutions of spectral problems for the Schrödinger operator on (−∞,∞) with polynomial potential

Makarov V. L.


Abstract

New exact representations for the solutions of numerous one-dimensional spectral problems for the Schr¨odinger operator with polynomial potential are obtained by using a technique based on the functional-discrete (FD) method. In cases where the ordinary FD-method is divergent, we propose to use its modification, which proved to be quite efficient. The obtained theoretical results are illustrated by numerical examples.

Citation Example: Makarov V. L. Exact and approximate solutions of spectral problems for the Schrödinger operator on (−∞,∞) with polynomial potential // Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 79-93.