Sobolev Orthogonal Polynomials for Solving the Schrödinger Equation with Potentials \(V(x)=x^{2k}\) , \(k\geqslant 1\)
摘要
When you deal with spectral methods for boundary value problems by using the variational formulation in the case of the one-dimensional Schrödinger equation, Sobolev inner products appear in a natural way. In this contribution we focus our attention on a sequence of Sobolev orthogonal polynomials associated with the Schrödinger equation for potential \(V(x)= x^{2k}, k\geqslant 1.\)