Estimates of parabolic cylinder functions on the real axis
Pokrovski, Alexis
Original · EN
We estimate simple combination of the parabolic cylinder functions and their derivatives. These estimates are important for the spectral analysis of non-analytically perturbed quantum harmonic oscillator. The estimates are valid in rather complicated domains and refine there the classical result of Olver. We determine the part of the real x-axis, which is within the domains of the estimates. This requires a detailed study of the image of the real x-axis in the standard quasiclassical variable.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.