TIMEDEPENDENT WKR EXPANSIONS FOR A CLASS OF PROPAGATORS S.M. BLINDER

A time-dependent variant of the WKB method is developed for propagators which do not have the simple Feynman structure K = jexp(iS/h) with j = j ( t). The method is applied to radial propagators for N-dimensional isotropic oscillators. An expansion in ascending powers of h results in an asymptotic series, which sums to a simple form involving a Bessel function. Alternatively, a convergent series for the propagator is obtained by expansion in inverse powers of tr. Semiclassical pproximations topropagators are extensively applied in spectroscopy, scattering theory, molecu-lar dynamics, irreversible thermodynamics and elementary-particle th ory [ 11. Terms in the WKB expansion in-volving higher powers of ti are less often considered. In this paper, we develop a time-dependent formulation of the WKB method which can be systematically extended to arbitrary powers of fi. The method is applied to the radial components of the Feymnan propagators for N-dimensional isotropic harmonic oscillators. Consider accordingly anN-dimensional Euclidean space (x1, x2...xN) with the generalized radial variable r = (1) For anN-dimensional isotropic harmonic oscillator, the partial-wave propagator for hyperangular momentum quantum number L satisfies the radial Schrijdinger equation N=2,3,4...; L=O,1,2, (2) subject o the initial conditio