共查询到20条相似文献,搜索用时 0 毫秒
1.
We discuss the perturbation of continuum eigenvalues without analyticity assumptions. Among our results, we show that generally a small perturbation removes these eigenvalues in accordance with Fermi's Golden Rule. Thus, generically (in a Baire category sense), the Schrödinger operator has no embedded non-threshold eigenvalues.Supported in part by NSF Grant DMS 8602826 相似文献
2.
A. Meykens P. Fettweis M. Nève de Mévergnies 《Zeitschrift für Physik A Hadrons and Nuclei》1978,284(4):417-423
The perturbation of the decay constant of90m Nb implanted in various transition metals (Zr, Nb, Hf, Ta, Ag and Au) has been determined by direct half-life measurements. Particular care was taken to evaluate and minimize possible systematic errors. The maximum relative change found is νAu?νNb/νNb=(4.5±0.8)% 相似文献
3.
David M. A. Stuart 《Communications in Mathematical Physics》1992,149(3):433-462
In this paper we prove the validity of formal asymptotic results on perturbation theory for kind solutions of the sine-Gordon equation, originally obtained by McLaughlin and Scott. We prove that for appropriate perturbations, of size in an appropriate norm, slowly varying in time in the rest frame of the kink, the shape of the kink is unaltered in theL
norm toO() for a time ofO(1/). The kink parameters, which represent its velocity and centre, evolve slowly in time in the way predicted by the asymptotics. The method of proof uses an orthogonal decomposition of the solution into an oscillatory part and a one-dimensional zero-mode term. The slow evolution of the kink parameters is chosen so as to suppress secular evolution of the zero-mode.Partially supported as a graduate student at Princeton University of NSF grant 215 6211 相似文献
4.
Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H0 + xV, where H0 is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators . We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and in powers of x is investigated. It is shown that W(x) and are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and which is closest to the origin and thus defines the radius r0 of convergence of the expansions of W and . It is shown that r0 is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W. 相似文献
5.
M.I. Jaghoub 《The European Physical Journal A - Hadrons and Nuclei》2002,15(4):443-448
In the presence of a velocity-dependent Kisslinger potential, the partial-wave, time-independent Schr?dinger equation with
real boundary conditions is written as an equation for the probability density. The changes in the bound-state energy eigenvalues
due to the addition of small perturbations in the local as well as the Kisslinger potentials are determined up to second order
in the perturbation. These changes are determined purely in terms of the unperturbed probability density, the perturbing local
potential, as well as the Kisslinger perturbing potential and its gradient. The dependence on the gradient of the Kisslinger
potential stresses the importance of a diffuse edge in nuclei. Two explicit examples are presented to examine the validity
of the perturbation formulas. The first assumes each of the local and velocity-dependent parts of the potential to be a finite
square well. In the second example, the velocity-dependent potential takes the form of a harmonic oscillator. In both cases
the energy eigenvalues are determined exactly and then by using perturbation theory. The agreement between the exact energy
eigenvalues and those obtained by perturbation theory is very satisfactory.
Received: 24 May 2002 / Accepted: 15 July 2002 / Published online: 3 December 2002
RID="a"
ID="a"e-mail: mij@hu.edu.jo
Communicated by V. Vento 相似文献
6.
Tucker Carrington Jr 《Molecular physics》2013,111(5):757-766
An efficient perturbative method is developed to facilitate the treatment of the anharmonicity of bending degrees of freedom. The Rosen-Morse and sec2 potentials are transformed so that perturbation theory may be applied easily. For a model problem it is found that the difference between the energy levels obtained from perturbation theory and the exact energy levels is less than 0·1 cm-1 for the first six energy levels. 相似文献
7.
An analytical equation of state is presented for the square-well dimer fluid of variable well width (1 ≤ λ ≥ 2) based on Barker-Henderson perturbation theory using the recently developed analytical expression for radial distribution function of hard dimers. The integral in the first- and the second-order perturbation terms utilizes the Tang, Y and Lu, B. C.-Y., 1994, J. chem. Phys., 100, 6665 formula for the Hilbert transform. To test the equation of state, NVT and Gibbs ensemble Monte Carlo simulations for square-well dimer fluids are performed for three different well widths (λ = 1.3, 1.5 and 1.8). The prediction of the perturbation theory is also compared with that of thermodynamic perturbation theory in which the equation of state for the square-well dimer is written in terms of that of square-well monomers and the contact value of the radial distribution function. 相似文献
8.
Perturbation theory is used to consider expansions for the radial distribution function, g 2(r), of a fluid with a soft core. We consider the Lennard-Jones (12, 6) potential and divide it into repulsive and attractive regions. In the repulsive region we expand the function exp (β u(r))g 2(r) about a hard sphere value. For the first-order contribution of the attractive region we consider a simple approximation to the exact analytical expression. The resulting g 2(r) is accurate at densities below about ρσ 3=0·5. 相似文献
9.
A perturbation expression for the angular pair correlation function g (2)(r 12, ω1, ω2) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g (2)(r 12, ω1, ω2) and the present expression is made for a system of two-dimensional point dipoles. 相似文献
10.
Marjan Baće 《Physics letters. [Part B]》1973,43(3):222-224
It is shown that the ln ? factors, found by Li and Pagels in perturbative expansions in ? around spontaneously broken chiral symmetry limits, become factors of ??1 in the dilaton in model. The method also furnishes an improved derivation of the Li-Pagels result. 相似文献
11.
In a previous paper second-order calculations were carried out on the two-level pairing force model using perturbation theory for projected states and the results were compared with those of BCS or ordinary perturbation theory. In the present paper criteria for convergence are applied to two different forms of the perturbation series for both the projected and ordinary perturbation theories. It is found that the superior results obtained for the convergence rates in the projected theory tally neatly with the results of the second-order calculations, and give further support to the use of the projected perturbation theory. 相似文献
12.
A technique for computing the thermodynamic (Matsubara) Green function for the Hubbard Hamiltonian as applied to the one-impurity
problem is proposed. There are only four states in this problem, which makes it solvable. 相似文献
13.
Michael Ram 《International Journal of Theoretical Physics》1970,3(2):153-164
We derive a very simple expression for the total decay rate of an unstable particle analogous to the optical theorem, and
demonstrate its equivalence with the total decay rate defined in terms of the imaginary part of the propagator pole. The common
origin of mass shifting and total decay rate is also demonstrated.
Work supported in part by grants from the Research Foundation of the State of New York and the National Science Foundation. 相似文献
14.
15.
Bernard M. De Dormale 《Reports on Mathematical Physics》1985,21(1):35-42
Proof of convergence of perturbation series for the S matrix elements is given for the relativistic Lee model, subject to the validity of an hypothesis explained in the paper. A proof of isometry for the wave operators is also given. 相似文献
16.
We apply perturbation theory to the gauge invariant version of the chiral Schwinger model. The cancellation of anomalies is shown explicitly in terms of Feynman diagrams. We calculate the exact propagators for the gauge field, for the Wess-Zumino field and for the mixing between these fields. Using these propagators, we demonstrate the existence of a massive state. 相似文献
17.
A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function. 相似文献
18.
Perturbation theory is applied suitably to obtain an expression, valid for all types of binding, for the shift in ground state energy of an electron bound to a coulomb impurity in a polar semiconductor. 相似文献
19.
Euclidean symmetric integration, previously proposed for the SU(N) Yang-Mills theory in the limit of large N, is used to study the propagators in the Schwinger model and the massive vector-meson model in two dimensions. The result of summing the perturbation series agrees with the exact solution in each case. Therefore, perturbation theory is here capable of dealing with non-analytic behaviour in the coupling constant. 相似文献
20.