Last edited by Miktilar
Wednesday, May 6, 2020 | History

2 edition of On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase. found in the catalog.

On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase.

Norman Levinson

# On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase.

## by Norman Levinson

Written in English

Subjects:
• Wave mechanics.

• Edition Notes

Classifications The Physical Object Series Danske videnskabernes selskab, Copenhagen. Matematisk-fysiske meddelelser,, bd. 25, nr. 9, Matematisk-fysiske meddelelser (Kongelige Danske videnskabernes selskab) ;, Bd. 25, nr. 9. LC Classifications AS281 .D215 bd. 25, nr. 9 Pagination 29 p. Number of Pages 29 Open Library OL198795M LC Control Number a 51001524 OCLC/WorldCa 19942020

This is a good property for an estimator to possess. It means that for any given distribution of the data, there is a sample size n su¢ ciently large such that the estimator will be arbitrarily close to the true value with high probability. Consistency is also an important preliminary step in establishing other important asymptotic Size: KB. A collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a wide variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is intended for graduate students in probability and statistics, and Price: $Asymptotic expansions for ordinary differential equations (Pure and applied mathematics) Hardcover – January 1, by Wolfgang Richard Wasow (Author) › Visit Amazon's Wolfgang Richard Wasow Page. Find all the books, read about the author, and more. Author: Wolfgang Richard Wasow. equation. (⁄2) Use iteration to ﬂnd the ﬂrst four terms in an asymptotic expan-sion of the negative root of x4 +†x3 = 1 for j†j ¿ 1. Find the ﬂrst three (non-zero) terms in an asymptotic expansion for the smallest (in size) solution of y5 +y3 +y2 ¡y = † for †! 0; by (a) using a trial expansion, (b) using an. located at the origin interacts with a matter density given by the square of the (real) wave function, which is the solution of the Sclirodiiiger equation. On the other hand, in the Sclirodiiiger equation a given potential energy is superposed with a gravita-tional energy obtained by solving Newton's law of gravitation. (The Scliiodiiiger-. As an example construct we asymptotic solutions of Laplace’s equation on a manifold with a second order caspidal singularity. The paper continues the research into asymptotic behaviour of solutions to equations with singularit carried out in a series of articles [2], [5], [6] and so on. In [5], asymptotic expansions for solutions to equations. Available for Download Share this book You might also like City of darkness City of darkness Conditions affecting roll-over of road tankers Conditions affecting roll-over of road tankers Keys For Writers With Webcard And Exercise Booklet Third Edition And Identities Keys For Writers With Webcard And Exercise Booklet Third Edition And Identities Philoctetes; the play and the man Philoctetes; the play and the man ceremonies of the Roman rite described ceremonies of the Roman rite described Early schooldays in Beaconsfield Early schooldays in Beaconsfield Paris Commune in French politics, 1871-1880 Paris Commune in French politics, 1871-1880 Close to home Close to home Some unpublished letters of Sir Walter Scott Some unpublished letters of Sir Walter Scott Front lines Front lines Mineral facts and problems Mineral facts and problems Some aspects of the acquisitions program at the University of Chicago Library, 1892-1928 Some aspects of the acquisitions program at the University of Chicago Library, 1892-1928 Health education Health education ### On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase by Norman Levinson Download PDF EPUB FB2 Ential equation in [1]. The setup of measuring an observable of the chain after each interaction is considered in [5], but the continuous limit, the ex-istence and the uniqueness of the solutions are not all treated rigorously in this reference. The aim of this article is to study the diﬀusive Belavkin equation, toCited by: In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f(n) as n becomes very large. If f(n) = n 2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n function f(n) is said to be "asymptotically equivalent to n. tion at inﬁnity to leading order up to a phase shift, and a central region in which long-time asymptotic behavior of the solution of the focusing NLS equation () is given by () q.x () and on the ratio x=tvia the stationary point k1deﬁned by equation (). For x>4 p 2qot, the leading-order asymptotic behavior of the File Size: 3MB. Asymptotic Analysis of the Local Potential Approximation to the Wetterich Equation Carl M Bendera;b and Sarben Sarkarby aDepartment of Physics, Washington University, St. Louis, MissouriUSA bDepartment of Physics, King’s College London, London WC2R 2LS, UK Abstract This paper reports a study of the nonlinear partial di erential equation that arises in the local. We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L 2 (ℝ) initial data. This is a preview of subscription content, log in to check by: THE ASYMPTOTIC SOLUTIONS OF THE GENERAL DIFFERENTIAL EQUATION 2. The given equation. A change of variables may be made to reduce the differential equation as given above to the normal form (1) u"(z)+ {p24>2(z) -x(z)}u(z) =0, and simultaneously to transfer to the origin the point at which the coefficient 4>2 vanishes. In this paper we consider a class of logarithmic Schrödinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some arguments of the Fountain theorem, and in the case of bounded potential we obtain a ground state solution, i.e. a nontrivial solution with least possible by: Abstract: We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation () for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L 2 (ℝ) initial use the method of Young measures and mollification by: (16) From the definition of M it is seen that Eq. (16) is a nonlinear partial differential equation of first order and degree 2(2L + 1) for the phase function f. This equation replaces the Hamilton-Jacobi equation which arises in a similar fashion from the usual W.K.B. theory which follows from (1). There may be more than one solution, f, of by: AN ASYMPTOTIC FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRODINGER EQUATION¨ WITH POLYNOMIAL POTENTIAL S. ALBEVERIO AND S. MAZZUCCHI Abstract. A functional integral representation for the weak so-lution of the Schr¨odinger equation with a polynomially growing potential is proposed in terms of an analytically continued Wiener integral. We introduce a new kind of equation, stochastic differential equations with self-exciting switching. Firstly, we give some preliminaries for this kind of equation, and then, we get the main results of our paper; that is, we gave the sufficient condition which can guarantee the existence and uniqueness of the : Guixin Hu, Ke Wang. We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for | x | > a and by an arbitrary function for | x | Cited by: 1. S-asymptotically ω-periodic solution for a nonlinear differential equation with piecewise constant argument in a Banach Available via license: CC BY-NC Content may be subject to. In this work we study the Cauchy problem of a fourth-order nonlinear Schrödinger equation which arises from certain physical applications. We consider only the cases n=1,2,3n=1,2,3. The asymptotic form for large$|t|$can be obtained by applying the method of stationary phase to the integral stated above. Since the phase$\vec{p}\cdot \vec{x}-\epsilon_{\vec{p}} t$is rapdily varying as function of$\vec{p}$when t (and possibly also$\vec{x}$is large, the dominant contribution to the integral comes from the point:$\vec{p.

The equation for the wave function can be reduced to ∇²φ = −J(z)φ(z) where φ²(z) must be normalized. The Classical Model. Consider again a particle of mass m moving in space whose position is denoted as z.

The potential field given by V(z) where V(0)=0 and V(−z)=V(z). () Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation. Nonlinear Analysis: Real World Applications() On a perturbed kernel in by: the solutions of the reduced equation of the given differential equation.

On the basis of the above remarks, a close relationship can already be ex-pected to exist between the theory of Langer and the present work in a fairly wide class of problems.

If, in the reduced equation (), a(0) is not an integer. The Asymptotic Limit of the The equation for the wave function can be reduced to Consider again a particle of mass m moving in one dimensional space whose position is denoted as x.

The potential field given by V(x) where V(0)=0 and V(−x)=V(x). Let v be the. ON THE ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS OF THE SCHRODINCER EQUATION kz)V= F YOSHIMI SAITO (Recieved October 1, ) 1.

Introduction Let us consider the Schrϋdinger operator () S=-A+Q(y) in RN. The purpose of this work is to show an asymptotic formula for the solution V of the equation (S—k2)V=F under the assumption that Q(y) is a.

"A book of great value it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding.is an asymptotic expansion (or an asymptotic approximation, or an asymptotic representation) of a function f(x) as x→ x0, if for each N.

f(x) = ∑N n=1 anφn(x)+o(φN(x)), as x→ x0. Note that, the last equation means that the remainder is smaller than the last term included once the diﬀerence x−x0 is suﬃciently Size: KB.and complete asymptotic description of the multiple pole solutions is given.

More precisely, the asymptotic paths of the solitons are determined and their position- and phase-shifts are computed explicitly. As a corollary we generalize the conservation law known for the N .