This is the first of a series of articles dealing with the casual use of distributions made by physicists and engineers. This use is very economical but sometimes leads to embarrassing conclusions that are difficult to justify with rigorous theories of distributions.

Existe uma situação tal que quando uma função ƒ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) é combinada com a função delta de Dirac, δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), a formula usual <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle"> deixa de ser válida. Uma situação similar pode ocorrer com a derivada da função delta, δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), com relação à formula <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. Nós apresentamos um apanhado destas situaçãoes não usuais e elucidamos os mecanismos por detrás delas. Nós discutimos as implicações destas situaçãoes em relação ao problema de tranmissão-reflexão em mecânica quântica uni-dimensional.

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.

Esta nota descreve uma questão sobre sistemas nao-holonômicos, um assunto que tem desaparecido de livros-texto e que ate mesmo tem sido tratado incorretamente como holonômico.

This note describes a question that deals with nonholonomic systems, a subject that has been gradually fading away from textbooks and even treated somewhat incorrectly as holonomic.

In a previous paper, we found the most general boundary conditions for the Aharonov -Bohm scattering of a Dirac particle. We found the resulting wave functions but we did not worry about delta normalizing them. As is well know, in practice, it is not easy to evaluate the diverging integrals occurring in the process. The purpose of this paper is to evaluate those integrals and present the resulting delta normalized eigenfunctions.