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

摘要

Transmission and reflection of a quantal particle by a single-hump potential barrier are analysed by means of an amplitude-phase decomposition of the wavefunction on both sides of the barrier. The amplitude-phase analysis of the wavefunction 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 for an Eckart-Epstein potential barrier provide very accurate results.