Barrier transmission problem treated by amplitude-phase method and expressed in terms of an invariant of the Ermakov-Lewis type

Authors: Thylwe, K.-E.
Document Type: Article
Pubstate: Published
Journal: J. Phys. A: Math. Gen
Volume: 38   235-243
Year: 2005


Transmission and reflection of a quantal particle by an Eckart-Epstein potential barrier is analysed by means of an amplitude-phase decomposition of the wave function on both sides of the barrier. The amplitude-phase analysis of the wave function provides a particular invariant of the Ermakov-Lewis type, which originates in the matching process. The transmission and reflection coefficients turn out to be simple functions of this invariant. Numerical calculations of the invariant provide very accurate results.