A model for the Schrödinger operator
Hermann Render (Gerhard-Mercator Universität Duisburg)
Discretizations of the Schrödinger Operator in the one-dimensional
case, i.e. of the Sturm-Liouville Operator, can be analysed by means
of orthogonal polynomials.
Further, by the theorem of M. Stone, these operators are unitarily
equivalent to a multiplication operator with a variable x on a Hilbert
space where is the spectral measure
of the operator.
In this talk, which is based on joint work with O. Kounchev (Bulgarian Academy of Sciences), we want to discuss representations of the Schrödinger
Operator as multiplication with on a Hilbert space
, where is a suitable non-negative measure
over and is the euclidean norm.
Special attention is devoted to semi-discretizations of the Schrödinger
operator on the strip and an explicit solution for the problem is given for
the case of separable potentials.