JWKB approximation

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

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

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. 

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

Frdman, A., and Ldwdin, P.-O. (1960). Preprint No. 51. Uppsala University, Uppsala. Fr6man, N., and Frdman, P. O. (1965). JWKB Approximation. North-Holland Publ., Amsterdam. 

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 

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