Exact solutions of spectral problems for the Schrödinger operator on (–∞, ∞) with polynomial potential obtained via the FD-method - Makarov, V.L. (Reports of the National Academy of Sciences of Ukraine, 2017)
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.