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arXiv · 0910.5829

The fractional Schr\"{o}dinger operator and Toeplitz matrices

Agapitos Hatzinikitas
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Abstract

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.

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Agapitos Hatzinikitas. 2009-10-30. The fractional Schr\"{o}dinger operator and Toeplitz matrices. https://doi.org/10.1063/1.3237146

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