Read e-book online Asymptotic solutions of the one-dimensional Schrödinger PDF

By S. Yu. Slavyanov

ISBN-10: 0821805363

ISBN-13: 9780821805367

This e-book is dedicated to asymptotic research of strategies of moment order traditional differential equations with a small parameter. the most emphasis is on a number of positive schemes of acquiring asymptotic ideas, their benefits and disadvantages, and particular computations. the writer offers a whole review of the kingdom of the idea and likewise concentrates on a few lesser recognized elements and difficulties, particularly the issues within which exponentially small phrases could be taken into consideration or the research of equations with shut transition issues. Such purposes because the derivation of the formulation for the quasiclassical quantizations, spectrum splitting in a symmetrical capability, etc., are thought of.

Show description

Read Online or Download Asymptotic solutions of the one-dimensional Schrödinger equation PDF

Similar differential equations books

Get The Analysis of Linear Partial Differential Operators. IV, PDF

From the studies: those volumes (III & IV) entire L. Hoermander's treatise on linear partial differential equations. They represent the main whole and updated account of this topic, by way of the writer who has ruled it and made the main major contributions within the final many years. .. .

Typical singularities of differential 1-forms and Pfaffian by Michail Zhitomirskii PDF

Singularities and the type of 1-forms and Pfaffian equations are attention-grabbing not just as classical difficulties, but additionally due to their purposes in touch geometry, partial differential equations, keep an eye on conception, nonholonomic dynamics, and variational difficulties. as well as amassing effects at the geometry of singularities and class of differential types and Pfaffian equations, this monograph discusses functions and heavily similar category difficulties.

Ayres F's Theory and Problems of Differential Equations Including 560 PDF

Could be shipped from US. Used books won't comprise significant other fabrics, could have a few shelf put on, might comprise highlighting/notes, won't contain CDs or entry codes. a hundred% a reimbursement warrantly.

Download e-book for kindle: Introductory differential equations with boundary value by Martha L. Abell, James P. Braselton

This article is for classes which are ordinarily referred to as (Introductory) Differential Equations, (Introductory) Partial Differential Equations, utilized arithmetic, and Fourier sequence. Differential Equations is a textual content that follows a conventional technique and is acceptable for a primary path in traditional differential equations (including Laplace transforms) and a moment path in Fourier sequence and boundary price difficulties.

Extra info for Asymptotic solutions of the one-dimensional Schrödinger equation

Example text

Zo. 10); that is, 11±(z) = z- 1/ 4 exp ( ± 2 · z 312/3). 22Y are defined by taking arithmetic values for positive arguments; 6(z) = 5/(16z2). Set c1 = 0, c2 = 1 and let the integration be from +oo to z. This will give us one of the solutions of the Airy equations, y- (z). As we will see, up to a multiplicative factor this solution coincides with Ai(z). 23) a(z) = 1 + : 2 12 { 1 - exp [4(z312 - ( 312)/3] }a(() d(. ()() We now change the variables as t = 2z3 / 2/3, s = 2(3 12/3 and define the function · a(t) = a(z).

Consider the contour integral I = I e-t2 /2+tzrv-1 dt, l defined for any value of a complex parameter v. The contour l, shown in Figure 7, encircles the cut ( -oo, OJ. If we fix the branch of the integrand by the condition arg(rv- 1 ) = 0 for argt = O, we can rewrite the above integral for Rev< 0 as J J 00 I= e-i'll"v e-t2/2-tzt-v-ldt _ ei'll"v 0 00 e-t 212-tzrv-ldt. 3. 3) I e-t2/2-tzrv-1 dt. 2) to the right halfplane of v. 2), and the extension to the rest of the complex v-plane will be carried out by the analytic continuation.

21) y(z) = c111+(z) :f- c211-(z) + J K(z,()6(()y(() d(, zo where 1 . K(z, () = W( 11+, 11 _) (11+(z)11-(() -11-(z)11+(()), and W (11+, 11-) is the Wronskian of 11+, 11-. It can be calculated explicitly: W(11+,11-) =11+11- 1 -11-11+ 1 = -2. Here z0 is either a fixed finite point or oo. 21) is carried out along a finite contour connecting the points zo and z. zo. 10); that is, 11±(z) = z- 1/ 4 exp ( ± 2 · z 312/3). 22Y are defined by taking arithmetic values for positive arguments; 6(z) = 5/(16z2).

Download PDF sample

Asymptotic solutions of the one-dimensional Schrödinger equation by S. Yu. Slavyanov


by Jason
4.0

Rated 4.20 of 5 – based on 15 votes