The fractional Schrödinger operator and Toeplitz matrices

Details The fractional Schrödinger operator and Toeplitz matrices The fractional Schrödinger operator and Toeplitz matrices

2009-10-30

arxiv.org/abs/0910.5829v1

J. Math. Phys. 50 (2009) 103524

Physics

Mathematical Physics

10 pages, 2 figures

Scientific paper

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.

Affiliated with

Also associated with

No associations

Rating

The fractional Schrödinger operator and Toeplitz matrices 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 The fractional Schrödinger operator and Toeplitz matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The fractional Schrödinger operator and Toeplitz matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-89578