The existence of wave operators for oscillating potentials

DOI10.1063/1.524678zbMath0452.35103OpenAlexW2067065573MaRDI QIDQ3898914

Allen Devinatz

Publication date: 1980

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.524678

zbMATH Keywords

Schrödinger operatorsasymptotic theoryshort range potentialMoller wave operators

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Szegő condition, scattering, and vibration of Krein strings, Erratum: Spectral and scattering theory for the adiabatic oscillator and related potentials [J. Math. Phys. 2 0, 594(1979)], A limiting absorption principle for Schrödinger operators with oscillating potentials. Part II: \(-\Delta+(c\sin b|x|)/|x|+V(x)\) for short range \(V\) and small coupling constant \(c\), Existence of the Møller wave operators in quantum scattering theory, Phase shifts and the modified and Møller wave operatos, A limiting absorption principle for Schrödinger operators with oscillating potentials. Part I: \(-\Delta +c \sin(b| x|^{\alpha})/| x|^{\beta}\) for certain c,\(\alpha\),\(\beta\), Quantum mechanical scattering theory for potentials of the form V(r) = (sin r)/r β , 1/3<β≤1/2

Cites Work

• Wave operators for oscillating potentials
• Existence of the Moller wave operators for \(V(\tau)={\lambda\sin (\mu r^\alpha )\over r^\beta}\)
• Asymptotic completeness for quantum mechanical potential scattering. I: Short range potentials
• Spectral and scattering theory for the adiabatic oscillator and related potentials
• Erratum: Spectral and scattering theory for the adiabatic oscillator and related potentials [J. Math. Phys. 2 0, 594(1979)]