caa a22 4500 388109181 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S030821050001310X doi S030821050001310X pii (NATIONALLICENCE)cambridge-10.1017/S030821050001310X Point transfer matrices for the Schrödinger equation: the algebraic theory [Elektronische Daten] This paper deals with the theory of point interactions for the one-dimensional Schrödinger equation. The familiar example of the δ-potential V(x) = gδ(x−x0), for which the transfer matrix across the singularity (point transfer matrix) is given by is extended to cover cases in which the transfer matrix M(z) is dependent on the (complex) spectral parameter z, and which can be obtained as limits of transfer matrices across finite intervals for sequences of approximating potentials Vn. The case of point transfer matrices polynomially dependent on z is treated in detail, with a complete characterization of such matrices and a proof of their factorization as products of point transfer matrices linearly dependent on z. The theory presented here has applications to the study of point interactions in quantum mechanics, and provides new classes of point interactions which can be obtained as limiting cases of regular potentials. Copyright © Royal Society of Edinburgh 1999 Gordon N. A. Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, UK Pearson D. B. Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, UK Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 717-732 0308-2105 129:4<717 1999 129 PRM https://doi.org/10.1017/S030821050001310X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030821050001310X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gordon N. A. Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, UK NATIONALLICENCE 700 1- Pearson D. B. Department of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, UK NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 717-732 0308-2105 129:4<717 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge