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Mecânica Quântica II
Aula 13
Fórmulas de Conexão da Aproximação WKB
Ref.: Griffiths, Int. Q.M., 2nd ed.
)( z )( z
(The term with b was set to zero by the use of the overlap in region 2 discussed
above)
so
It is possible to deduce the WKB connection formulas without using the Airy
functions or their asymptotic expressions.
This can be done by using contour integration in the complex plane,
assuming that x is a complex variable.
This way, it is possible to avoid the classical turning points and then evaluate
the WKB integrals in the complex plane.
The original reference is A. Zwaan, Thesis, Utrecht, 1929.
For a review see Landau & Lifishitz, Quantum Mechanics, Non-Relativistic
Theory, 3rd ed., section 48, pgs. 167-170.
See also L. A. Young and G. E. Uhlenbeck , Phys. Rev. 36, 1154–1167 (1930)
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