JWKB approximation

We share the opinion expressed by Farrelly and Reinhardt (1983) that discrepancies between Stark effect results obtained by the use of the Carlini (JWKB) approximation and by accurate numerical calculations cannot be attributed to the break-down of the approximation, but are due to a failure to use the approximation in a correct way. An appropriate approach based on the phase-integral approximation of arbitrary order generated from an appropriately chosen base function is a still more efficient and often highly accurate method for the treatment of several problems, not only in quantum mechanics, but in various fields of theoretical physics. With... 

When one derives the Carlini (JWKB) approximation one introduces a factor 1/A2 in front of R(z) in the differential equation (4.1) and puts... 

Froman, N., and Froman, P. O., 1965, JWKB Approximation, Contributions to the Theory. North-Holland Publishing Company, Amsterdam. Russian translation MIR, Moscow 1967. 

N. Fromanand P. O. Froman, JWKB Approximation, North-Holland, Amsterdam, 1965. 

The phase shifts rji are calculated by the method of JWKB approximation with Langer s modification - ... 

When the collision energy E is sufficiently large, so there are no threshold effects, the JWKB approximation is an excellent approximation at all R, and the form of... 

The WKB approximation, which is sometimes called the JWKB approximation, paying respect to the contribution of mathematician H. Jeffreys, provides us with the analytical expression of wave function for a particle moving in a general potential y(jc) as... 

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