Node Theorem for Matrix Schroedinger Operators

Details Node Theorem for Matrix Schroedinger Operators Node Theorem for Matrix Schroedinger Operators

1996-06-14

arxiv.org/abs/funct-an/9606003v2

Mathematics

Operator Algebras

The paper has been withdrawn because an error has occurred in the combinatorial estimates of the cluster expansion. It will be

Scientific paper

In this paper we study the ground states of a matrix Schroedinger operator, that is an operator of the type (-Laplace) + V acting on m-component wave functions in R^n. We prove in generalization of the classical node theorem that the ground states of this operator have no zeros, if the potential V satisfies the following conditions: 1) V is bounded from below. 2) V is strictly positive at infinity with respect to the ground state energy. 3) The partial derivatives of V do not grow too fast in the order of the derivative. Furthermore we show that the degeneracy of the ground states is at most m. For the proof we reformulate the problem with path integrals and perform a cluster expansion with large/small field conditions.

Affiliated with

Also associated with

No associations

Rating

Node Theorem for Matrix Schroedinger Operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Node Theorem for Matrix Schroedinger Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Node Theorem for Matrix Schroedinger Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-189633