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

1Makarov, VL
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 2:10-15
Section: Mathematics
Language: Ukrainian

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.

Keywords: exact eigenvalues, exponentially convergent method, Schrödinger operator, spectral problem
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