High-energy homogenization of a multidimensional nonstationary Schrödinger equation

2023/01/14 by Mark Dorodnyi, Dorodnyi, Mark · 1 citation
Computer Science · Mathematics · #35B27 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2301.05907

openalex publication_date 2023/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In L₂(ℝ^d), we consider an elliptic differential operator A_ε = - div g(x/ε) ∇ + ε^-2 V(x/ε), ε > 0, with periodic coefficients. For the nonstationary Schrödinger equation with the Hamiltonian A_ε, analogs of homogenization problems related to an arbitrary point of the dispersion relation of the operator A₁ are studied (the so called high-energy homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in L₂(ℝ^d)-norm for small ε are obtained.

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