Summary
A detailed analytical study is carried out of the problem for the reflection of a particle off a reflecting surface inquantum mechanics. We use the method of Green’s functions with suitable boundary conditions. A careful analysis is given to answer the question: where do the reflections actually occur on the reflecting surface? In particular, it is shown that, in answering the latter question, the reflecting surface is equivalent to a purely geometrical imaginary surface which merely «constraints» the possible quantum-mechanical «paths» of a particle on or above it.
Riassunto
Si svolge uno studio analitico dettagliato del problema della riflessione di una particella da una superficie riflettente nella meccanica quantistica. Si usa il metodo delle funizioni di Green con appropriate conditioni al contorno. Si esegue un’analisi dettagliata al fine di rispondere alla seguente domanda: dove si verificano effettivamente le riflessioni sulla superficie riflettente? In particolare, si mostra, nel rispondere a questa domanda, che la superficie riflettente è equivalente ad una superficie immaginaria puramente geometrica, che soltanto limita le possibili traiettorie quanto meccaniche di una particella sopra o al di sopra di essa.
Резюме
Проводится подробное аналитическое исследование проблемы отраженния частиц от отражающей поверхности в квантовой механике. Мы используем метод функций Грина с соответствующими граничними условиями. Подробно обсуждается вопрос: где в действительности происходит отражение на отражающей поверхности? В частности, показывается, что отражающая поверхность является чисто геометрической мнимой поверхностью, которая просто «ограничивает» возможные квантовомеханичекие «траектории» частиц на или над ней.
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Work supported by the Department of National Defence under CRAD No. 3610-637: F4122.
Traduzione a cura della Redazione.
Перевебено ребакцией.
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Manoukian, E.B. Reflection off a reflecting surface in quantum mechanics: Where do the reflections actually occur?. Nuovo Cim B 99, 133–143 (1987). https://doi.org/10.1007/BF02726576
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DOI: https://doi.org/10.1007/BF02726576