Exact and Approximate Solutions of the Spectral Problems for the Differential Schrödinger Operator with Polynomial Potential in ℝK, K ≥ 2

Resumo

We consider spectral problems for the Schrödinger operator with polynomial potentials in ℝ^K, K ≥ 2. By using a functional-discrete (FD-)method and the Maple computer algebra system, we determine a series of exact least eigenvalues for the potentials of special form. In the case where the traditional FD-method is divergent (the degree of the polynomial potential exceeds 2 at least in one variable), we propose a modification of the method, which proves to be quite efficient for the class of problems under consideration. The obtained theoretical results are illustrated by numerical examples.