Exponential decay for the eigenfunctions of the two body relativistic Hamiltonian (Q580597)

The main result of this work is a theorem which establishes \(L^ p\)- exponential decay (p\(\in]1,\infty [)\) for solutions u of the equation \((P-E)u=f\) in \({\mathbb{R}}^ n\), where \(P=(1-\Delta)^{1/2}+V\), \(E\in]0,1[\), f is a sufficiently regular function which decays exponentially and the potential V converges to zero at infinity and satisfies certain well-defined regularity properties. The result implies that the eigenfunctions of the two body relativistic quantum mechanical Hamiltonian P decay exponentially.