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}
}
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References

SHOWING 1-10 OF 73 REFERENCES
Pointwise bounds for Schrödinger eigenstates
TLDR
Using probabilistic techniques the authors prove pointwise upper bounds for Lq-Schrödinger eigenstates and pointwise lower bounds for the corresponding groundstate and generalize Schnol's and Simon's ones.
Exponential decay for the eigenfunctions of the two body relativistic hamiltonian
AbstractAn exponential decay result for the solutionsu of the equation $$(\sqrt {1 - \Delta } + V)u = f$$ is proved under the hypotheses thatV converges to zero at infinity andf decays
Perturbation of translation invariant positivity preserving semigroups on
The theory of singular local perturbations of translation invariant positivity preserving semigroups on L2(R", d"x) is developed. A powerful approximation theorem is proved which allows the treatment
Brownian local time and quantum mechanics
LetV be any (sufficiently regular) attractive potential in one and two dimensions. We make rigorous an argument of M. Kac [1], relating the recurrence of the Brownian motion to the existence of at
Relativistic Stability of Matter - I
In this article, we study the quantum mechanics of N electrons and M nuclei interacting by Coulomb forces. Motivated by an important idea of Chandrasekhar and following Herbst [H], we modify the
An uncertainty principle for fermions with generalized kinetic energy
AbstractWe derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltoniansh=f(−i∇)+V(x) acting onL2(ℝn). These bounds are then
Spectral theory of the operator (p2+m2)1/2−Ze2/r
Using dilation invariance and dilation analytic techniques, and with the help of a new virial theorem, we give a detailed description of the spectral properties of the operator (p2+m2)1/2−Ze2/r. In
The stability and instability of relativistic matter
We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namely p 2/2m is replaced by (p
...
1
2
3
4
5
...