Exact solutions of spectral problems for the Schrödinger operator on (–∞, ∞) with polynomial potential obtained via the FD-method

TitleExact solutions of spectral problems for the Schrödinger operator on (–∞, ∞) with polynomial potential obtained via the FD-method
Publication TypeJournal Article
Year of Publication2017
AuthorsMakarov, VL
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.02.010
Issue2
SectionMathematics
Pagination10-15
Date Published2/2017
LanguageUkrainian
Abstract

The functionally-discrete method is applied for the first time to derive exact solutions of one-dimensional spect ral problems for the Schrödinger operator with polynomial potential. This numerical-analytical method is capable of obtaining the solution in a closed form (as a result of the limit transition) or approximating the solution to any predescribed accuracy, when the close-form solution is impossible. The results, in particular, can be used to find the ground and excited energy states of anharmonic oscillators and oscillators with the double-well potential.
Keywordsexact eigenvalues, exponentially convergent method, Schrödinger operator, spectral problem
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