Completeness of wave operators in relativistic quantum mechanics

A. Soffer

doi:10.1007/BF00400982

Completeness of wave operators in relativistic quantum mechanics

A. Soffer

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schrödinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)² operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states 'trapped' inside some hyperboloid for all times.

Original language	English (US)
Pages (from-to)	517-527
Number of pages	11
Journal	Letters in Mathematical Physics
Volume	8
Issue number	6
DOIs	https://doi.org/10.1007/BF00400982
State	Published - Nov 1984
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF00400982

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title = "Completeness of wave operators in relativistic quantum mechanics",

abstract = "A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schr{\"o}dinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)2 operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states 'trapped' inside some hyperboloid for all times.",

author = "A. Soffer",

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N2 - A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schrödinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)2 operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states 'trapped' inside some hyperboloid for all times.

AB - A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schrödinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)2 operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states 'trapped' inside some hyperboloid for all times.

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Completeness of wave operators in relativistic quantum mechanics

Abstract

All Science Journal Classification (ASJC) codes

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