Bound level in a potential

In order to take care of the problem that yJWKB is not a good approximation near the turning points, it is necessary to define yusc(f ), USC indicating uniform semiclassical wavefunction (Miller and Good, 1953 Langer, 1937 Miller, 1968), which is uniformly valid close to or far from the turning points 

Thus xusc is constructed so that when R is in the classical region but far from a turning point, xusc(-R) = xJWKB(A). Note also that for a linear potential, 

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