3D Schr "odinger equation: scattering operator, scattering amplitude and\n ergodic property

2019/05/18 by Lev Sakhnovich, Sakhnovich, Lev
Mathematics · Physics and Astronomy · #34L25 #81Q05 #81Q30 #81T15 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1905.07608

openalex publication_date 2019/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stationary scattering problem (when the distance r tends to infinity) and\ndynamical scattering problem (when the time t tends to infinity) are\nconsidered for the 3D Schr "odinger equation. A simple interconnection between\nthe scattering amplitude (stationary case) and scattering operator (dynamical\ncase) is given in the paper. This result is a quantum mechanical analog of the\nergodic formulas in the classical mechanics.\n

Citations

• Relativistic Lippmann - Schwinger equation
• Eigenfunction expansions and scattering theory associated with Dirac\n equation

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