Exact solutions of spectral problems for the Schrödinger operator on (–∞, ∞) with polynomial potential obtained via the FD-method
DOI:
https://doi.org/10.15407/dopovidi2017.02.010Keywords:
exact eigenvalues, exponentially convergent method, Schrödinger operator, spectral problemAbstract
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.
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