M. Langer and C. Tretter,
Variational principles for eigenvalues of the Klein–Gordon equation,
J. Math. Phys. 47 (2006), 103506, 18 pp.
Abstract:
In this paper variational principles for eigenvalues of an abstract model of the
Klein–Gordon equation with electromagnetic potential are established.
They are used to characterize and estimate eigenvalues in cases where the essential spectrum
has a gap around 0, even in the presence of complex eigenvalues.
As a consequence, a comparison between eigenvalues of the Klein–Gordon equation
in ℝd and eigenvalues of certain Schrödinger operators is obtained.
The results are illustrated on examples including the Klein–Gordon equation with
Coulomb and square-well potential.