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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
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-0149-341X
2005 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, Vol. 38, no 1, 235-243 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2005. Vol. 38, no 1, 235-243 p.
Keyword [en]
dependent harmonic-oscillator, dimensional schrodinger equation, rapid numerical solution, differential-equation, potential barrier, wave mechanics, systems, energies, formulas, particle
Identifiers
URN: urn:nbn:se:kth:diva-14483ISI: 000226648800020Scopus ID: 2-s2.0-11844307223OAI: oai:DiVA.org:kth-14483DiVA: diva2:332524
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Thylwe, Karl-Erik

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