Abstract
In this note we give a variational characterization of the eigenvalues and eigenvectors for the operator
where H0) is the relativistic (free) Hamiltonian operator and V is a real valued potential. Our results hold when \(V(x) = \frac{1}{{\left| x \right|}}\) and H describe a relativistic atom. The characterization we give for the eigenvectors is useful in proving regularity and exponential decay of the solutions — properties which have been object of investigation by B. Simon with different techniques.
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Research partially supported by MIUR grant PRIN 201274FYK7, “Variational and perturbative aspects of nonlinear differential problems”. One of the Authors (V. Coti Zelati) is also partially supported by Program STAR, UniNA and Compagnia di San Paolo.
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Zelati, V.C., Nolasco, M. A Variational Approach to the Eigenfunctions of the One Particle Relativistic Hamiltonian. J Elliptic Parabol Equ 1, 89–108 (2015). https://doi.org/10.1007/BF03377370
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DOI: https://doi.org/10.1007/BF03377370