An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants

Details An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants

2009-03-09

arxiv.org/abs/0903.1402v2

Physics

Mathematical Physics

Scientific paper

In this paper, we investigate the three-dimensional Schrodinger operator with a periodic, relative to a lattice {\Omega} of R3, potential q. A special class V of the periodic potentials is constructed, which is easily and constructively determined from the spectral invariants. First, we give an algorithm for the unique determination of the potential q in V of the three-dimensional Schrodinger operator from the spectral invariants that were determined constructively from the given Bloch eigenvalues. Then we consider the stability of the algorithm with respect to the spectral invariants and Bloch eigenvalues. Finally, we prove that there are no other periodic potentials in the set of large class of functions whose Bloch eigenvalues coincides with the Bloch eigenvalues of q in V.

Affiliated with

Also associated with

No associations

Rating

An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants 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 An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Algorithm for Finding the Periodic Potential of the Three-dimensional Schrodinger Operator from the Spectral Invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-95092