# Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions

@article{Carmona1990RelativisticSO, title={Relativistic Schr{\"o}dinger operators: Asymptotic behavior of the eigenfunctions}, author={Ren{\'e} A. Carmona and W. C. Masters and Barry Simon}, journal={Journal of Functional Analysis}, year={1990}, volume={91}, pages={117-142} }

## 234 Citations

Path integrals for relativistic Schrodinger operators

- Mathematics
- 1989

Path integral methods for the investigation of the properties of Schrodinger operators go back to the pioneering works of Feynman and Kac. They have been successfully used for a long time but they…

Unicity of the integrated density of states for relativistic Schroedinger operators with regular fields and singular electric potentials

- Mathematics, Physics
- 2009

We show coincidence of the two definitions of the integrated density of states (IDS) for a class of relativistic Schroedinger operators with magnetic fields and scalar potentials, the first one…

Eigenfunctions decay for magnetic pseudodifferential operators

- Mathematics
- 2011

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated with discrete eigenvalues, for a class of self-adjoint operators in L2(Rd) defined by…

Probabilistic Representation and FallOff of Bound States of Relativistic Schrödinger Operators with Spin 1 / 2

- Mathematics, Physics
- 2021

A Feynman-Kac type formula of relativistic Schrödinger operators with unbounded vector potential and spin 1/2 is given in terms of a three-component process consisting of Brownian motion, a Poisson…

Magnetic Relativistic Schrödinger Operators and \\Imaginary-time Path Integrals

- Mathematics, Physics
- 2013

Three magnetic relativistic Schrodinger operators corresponding to the classical relativistic Hamiltonian symbol with magnetic vector and electric scalar potentials are considered, dependent on how…

Perturbations of Generalized Schrödinger Operators in Stochastic Spectral Analysis

- Mathematics
- 1992

The objective of stochastic spectral analysis is explained. It is used to study regular perturbations for a general class of generators of Feller semigroups, also called generalized Schrodinger…

Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators

- Mathematics
- 2016

Probabilistic Representation and Fall-Off of Bound States of Relativistic Schr\

- Mathematics, Physics
- 2011

A Feynman-Kac type formula of relativistic Schrodinger operators with unbounded
vector potential and spin 1/2 is given in terms of a three-component process consisting
of Brownian motion, a Poisson…

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