asymptotic evaluation, integrals, wavefunctions
An improvement in a previous procedure for the analytic asymptotic evaluation of integrals arising in the quantum-mechanical theory of inelastic molecular collisions is presented. The integrals are evaluated using Langer's uniform asymptotic wavefunctions and the higher-order saddle-point or steepest-descents method. It is found that the Langer functions give no better results than WKB functions, but the higher-order steepest-descents corrections produce a marked improvement. The result is a simple method for evaluating a large class of integrals with an error of 0.1%-2.1%.
Original Publication Citation
Smith, Wesley D. and Russell T. Pack. "Asymptotic Evaluation of WKB Matrix Elements. II. Use of Langer's Uniform Asymptotic Wavefunctions." The Journal of Chemical Physics 52 (197): 1381-1386.
BYU ScholarsArchive Citation
Smith, Wesley D. and Pack, Russell T., "Asymptotic Evaluation of WKB Matrix Elements. II. Use of Langer's Uniform Asymptotic Wavefunctions" (1970). Faculty Publications. 798.
Physical and Mathematical Sciences
Chemistry and Biochemistry
© 1970 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://link.aip.org/link/?JCPSA6/52/1381/1
Copyright Use Information