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)