An Asymptotic Study of a Glass of Ordinary Linear Differential Equations of the Second Order

[摘要] The asymptotic behavior, with respect to the large parameter µ,of two solutions of d²y/dx² + µ² [c² - x² + f(x, µ^-1)] y = 0 is givenwhere f(x, µ^-1) = 0(µ^-1) is subjected to suitable hypotheses and allvariables are real. These solutions are approximated to by the paraboliccylinder functions D_v(±√2µ t) with v = µ a²/2 - 1/2 and t = Ø(x,µ^-1).The function Ø(x,µ^-1) and the quantity a² are constructed as a part ofthe analysis in which the parameter µ is restricted in such a waythat v is bounded away from the positive integers. The relative errorof the approximating functions is uniform for all x.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics