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
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References
SHOWING 1-10 OF 73 REFERENCES
Pointwise bounds for Schrödinger eigenstates
- Mathematics, Computer Science
- 1978
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
- Physics, Mathematics
- 1986
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
- Mathematics
- 1978
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
- Mathematics, Physics
- 1986
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
- Physics
- 1986
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
- Physics
- 1983
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
- Mathematics
- 1977
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
- Physics
- 1988
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…