Spherical Schrödinger Hamiltonians: Spectral Analysis and Time Decay

2016/11/15 by Luca Fanelli, Fanelli, Luca
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1611.04805

16 pages. Survey for the forthcoming INdAM-Springer volume "Advances in Quantum Mechanics"

arxiv created 2016/11/15 · openalex publication_date 2016/11/15 · arxiv updated 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this survey, we review recent results concerning the canonical dispersive flow e^itH led by a Schrödinger Hamiltonian H. We study, in particular, how the time decay of space L^p-norms depends on the frequency localization of the initial datum with respect to the some suitable spherical expansion. A quite complete description of the phenomenon is given in terms of the eigenvalues and eigenfunctions of the restriction of H to the unit sphere, and a comparison with some uncertainty inequality is presented.

Citations

• Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential

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