Karl-Erik Thylwe 2005 J. Phys. A: Math. Gen. 38 235 doi:10.1088/0305-4470/38/1/017
The barrier transmission problem treated by the amplitude-phase method and expressed in terms of an invariant of the Ermakov–Lewis type
Karl-Erik Thylwe
Show affiliationsTransmission 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.
- PACS
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03.65.Ge Solutions of wave equations: bound states
- MSC
- Subjects
- Dates
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Issue 1 (7 January 2005)
Received 6 April 2004, in final form 15 October 2004
Published 8 December 2004
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The barrier transmission problem treated by the amplitude-phase method and expressed in terms of an invariant of the Ermakov–Lewis type
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