One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Fundacao de Amparo a Pesquisa do Estado de Sao Paulo

Fundacao de Amparo a Pesquisa do Estado de Sao Paulo

Natural Sciences and Engineering Research Council of Canada

Natural Sciences and Engineering Research Council of Canada

Japan Society for the Promotion of Science

Japan Society for the Promotion of Science (Japan)