The Cauchy problem of the one dimensional Schrödinger equation with non‐local potentials

Abstract

ABSTRACT. For a large class of operators A, not necessarily local, it is proved that the Cauchy problem of the SchrSdinger equation:

A “discretization” technique for the solution of ODEs

“…This technique was also used in [4][5][6][7][8][9][10][11], for the investigation of analytic and entire solutions of linear ODEs and in [12,13], it was extended to the study of non-linear ODEs, for non-linearities which were powers of the unknown function. In [14,15], the technique was further extended in order to include other kinds of nonlinearities.…”

“…The main idea of this functional-analytic technique used in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] is the transformation of the ODE under consideration, into an equivalent operator equation in an abstract Hilbert (H ) or Banach (H 1 ) space, using an isomorphism between H 2 (D) and H or H 1 (D) and H 1 .…”

Αναλυτικες Λυσεις Συνηθων Διαφορικων Εξισωσεων

“…Στο παρόν κεφάλαιο δίνονται συνθήκες ύπαρ ξης και μοναδικότητας αναλυτικών λύσεων του πιο πάνω προβλή ματος. Ενα μεγάλο μέρος του κεφαλαίου αυτού έχει δημοσιευ τεί [31].…”