Connection of Close Quarters to Generalized Turning Points.
Abstract
The solutions of Schroedinger equations have well-known WKB-approximations, but the coefficients in these differ on the two sides of a turning point. A new method for connecting them across such points is developed to extend present theory to a more general class of turning points, which includes logarithmic branch points of q(z), among many others. To this end, a delicate contraction for an integral equation differing from those of Langer and Olver is used to show that Bessel functions can still approximate the solutions at a certain, small distance from the irregular point of above Schroedinger equation even though not uniformly near it. A novel feature of the analysis is that the extreme variation of the exponential kernel is here controlled even on non-progressive paths. Connection is completed radially by means of the same integral equation.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1980
- Accession Number
- ADA086384
Entities
People
- J. F. Painter
- R. E. Meyer
Organizations
- University of Wisconsin–Madison