Related papers: The Schrodinger-HJW Theorem
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof.…
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
In 1994, P.-G. Becker and W. Bergweiler listed all the differentially algebraic solutions of three famous functional equations: the Schr{\"o}der's, B{\"o}ttcher's and Abel's equations. The proof of this theorem combines various domains of…
We apply technique developed in [2] to study the long-time behavior of Schrodinger evolution.
This short paper focuses on Schr\"oder's contribute towards a structural view of group theory.
A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys. \textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schr\"odinger equation is presented. Equations are further simplified and generalized for computing wave…
In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.
Several aspects of the time-dependent Schrodinger equation are discussed in the context of Quantum Information Theory.
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
This paper presents a proof of Gallai's Theorem, adapted from A. Soifer's presentation in The Mathematical Coloring Book of E. Witt's 1952 proof of Gallai's Theorem.
The paper deals with continuous solutions of a Schilling's problem.
The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb…
We give a concise introduction to the theory of continuants and show how Perron used them in his proof of Tietze theorem on the convergence of infinite semi-regular continued fractions, as well as for the study of the convergence of purely…
The work studies some Difference equations, which are connected with Mejer's function.
In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
In the recent paper, Ref. 1, the l-waves Schr\"odinger equation for the Cornell's potential is solved in quantum mechanics with a generalized uncertainty principle by following Ref. 2. It is showed here that the approach of Ref. 2 can only…