Single point interactions, quantization by parts, and boundary conditions

Traditionally point interaction problems in quantum mechanics are treated in the physics literature by solving the Schrodinger equation containing an appropriate potential term. In this paper we discuss a systematic quantization scheme, known as the method of quantization by parts, which provides a general method for dealing with single point interactions in one dimension, namely by reducing the problem to boundary conditions. Our method can also be applied to superconducting systems like those concerning Josephson and the recently discovered pi-junctions, and single electron circuit systems. (C) 2000 American Institute of Physics. [S0022-2488(00)02301-X].