The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only sour...

We test the Salpeter formalism for the electron screening of the solar proton-proton fusion reaction by solving numerically the relevant Schrödinger equation. We evaluate exactly the square of the overlap integral of the two-proton wave function and the deuteron wave function and compare with the usual analytic approximation. The usual WKB solution agrees with the numerical result to O(10). The...

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lamé potential (derived from representations of a finite dimensional matrix expressed in terms of su(2) generators) with the results of the tight–binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lamé potential ...

A novel WKB approach to calculating the lifetime of quasistationary states in the potential wells of the form V(x)=P(x)-muQ(x), where P(x) is the radial part of the potential for the spherically symmetric harmonic oscillator or the hydrogen atom and Q(x) is a polynomial, is suggested. In this approach, the usual explicit procedure of the asymptotic matching of the perturbative and WKB wave func...

In this paper we present a WKB approximation for sphericallysymmetric solutions of the Schrödinger-Newton equations. These are nonlinear modifications of the ordinary Schrödinger equation involving gravitational selfinteraction of the wavefunction. Applying the WKB procedure leads to two different nonlinear differential equations for the gravitational potential U for positive and negative value...

We study the spectrum of the reggeized gluon compound states in high-energy QCD. The energy of the states depends on the total set of quantum numbers whose values are constrained by the quantization conditions. To establish their explicit form we apply the methods of nonlinear WKB analysis to the Schrödinger equation for the N reggeon state in the separated coordinates. We solve the quantizatio...

Restricted detour distance between two vertices and of a graph is the length longest u- v path for induced condition (V (P))=P. The restricted polynomial depends on denoted by D*(G,x) defined = ∑{u,v}xD*(u,v) where summation taken over all unordered pairs (u,v) distinct u V(G). In this paper, we investigate straight chain wheel graphs φ(WkB) compute index φ(WkB).

WKB analysis of higher order Painlevé equations with a large parameter. II. — Structure theorem for instanton-type solutions of (P J) m (J = I, 34, II-2 or IV) near a simple P-turning point of the first kind

We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.