TOLOZA Julio Hugo
Exponentially accurate error estimates of quasiclassical eigenvalues. II. Several dimensions
JULIO H. TOLOZA
JOURNAL OF MATHEMATICAL PHYSICS
American Institute of Physics
Lugar: Melville; Año: 2003 vol. 44 p. 2806 - 2806
We study the behavior of truncated Rayleigh?Schrödinger series for low-lying eigenvalues of the time-independent Schrödinger equation, in the semiclassical limit of the Planck´s constant going to 0. In particular we prove that if the potential energy satisfies certain conditions, there is an optimal truncation of the series for the eigenvalues, in the sense that this truncation is exponentially close to the exact eigenvalue. These results were already discussed for the one-dimensional case in a previous article. This time we consider the multi-dimensional problem, where degeneracy plays a central role.