Unusual situations that arise with the Dirac delta function and its derivative Journal Articles uri icon

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abstract

  • There is a situation such that, when a function ƒ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) is combined with the Dirac delta function δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), the usual formula <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle">does not hold. A similar situation may also be encountered with the derivative of the delta function δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), regarding the validity of <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. We present an overview of such unusual situations and elucidate their underlying mechanisms. We discuss implications of the situations regarding the transmission-reflection problem of one-dimensional quantum mechanics.

publication date

  • December 2009