Perturbation theory with a tridiagonal zeroth-order hamiltonian

We generalize the Rayleigh-Schrödinger perturbation formalism to the hamiltonians H=H₀+λH₁ where the correction λH₁ is small and the unperturbed operator H₀ is represented by an infinite tridiagonal matrix. This enables us to construct the solutions E=E₀+λE₁+λ²E₂+… and |ψ〉 = |ψ₀〉+λ|ψ₁〉+λ²|ψ₂〉+… in terms of the analytic continued fractions.     

Perturbation theory for a bound polaron

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.     

Perturbation theory for a polarizing liquid

The thermodynamic perturbation theory is applied to polar polarizing liquids. A system of rigid dipoles is chosen as a basis, and the magnitude of the dipole moment is determined from the Gibbs-Bogolyubov variational principle. The equation of state obtained within the framework of the variational approach is used for calculating the free energy of a model system of polarizing dipolar solid spheres. Good agreement is obtained with results of computer experiment.     

Many-time hamiltonian gravitation theory

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

Perturbation theory for a bound piezoelectric polaron

We calculate the change in energy of an electron bound to a Coloumb center, due to the piezoelectric interaction with acoustic phonons, to second-order in the interaction. We show that the recent calculation by Bajaj et al., while correct to order β², is incorrect to order β⁴. β is the strength of the Coloumb potential. The coefficient of the β⁴ term is shown to be divergent.     

Perturbation theory for kinds

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     

Perturbation theory for a mixture of polarizable liquids

Thermodynamic perturbation theory developed for pure polar liquids with significant polarizability is applied to a mixture with polar and nonpolar polarizable components. Expressions for the average and unperturbed dipole moments of the components of the mixture are presented and the dipole and induced contributions to the thermodynamic functions of the mixture are calculated. The equation of state is obtained and used to calculate the excess properties of a binary mixture of particles interacting with a stockmeyer potential. It is shown that the induced dipole moments contribute significantly to the thermodynamic properties of this model solution and that their effects must be taken into account in predicting the properties of real liquid mixtures containing polar components.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 69–73, March, 1985.     

Perturbation theory for velocity-dependent potentials

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     

Perturbation theory for bending potentials

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.     

Multimomentum hamiltonian formalism in quantum field theory

The familiar generating functional in quantum field theory fail to be true measures and make sense only in framework of perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.     

The Multimomentum hamiltonian formalism in gauge theory

We extend the jet bundle machinery of gauge theory to the multimomentum Hamiltonian formalism. This enables us to manipulate finite-dimensional momentum spaces of fields. In the framework of this formalism, time and spatial coordinates are regarded on the same footing, and a preliminary (3 + 1) splitting of a world manifold is not required. We get the canonical splitting of a multimomentum Hamiltonian form into a connection part and a Hamiltonian density.     

Eigenfunctions of a model hamiltonian in the theory of a multielectron atom

The eigenfunctions of the model Hamiltonian discussed in a previous paper are found for the discrete and continuous spectra. These functions are used to calculate the oscillator strengths of the 2s-2p and 2s-3p transitions for Li, and a simple analytic equation is found for the oscillator strengths of the 2s-2p transition for lithium-like ions. The calculation errors is estimated to be 1–2%.Translated from Izvestiya VUZ. Fizika, No. 8, pp. 124–127, August, 1970.     

Perturbation theory for a microemulsion with triangular well potential

The perturbation approach of Barker and Henderson (1967, 1968) has been applied to a microemulsion obeying triangular well potential as a perturbative attractive tail over the Percus-Yevick (PY) hard sphere model by calculating the Rayleigh ratio,R ₉₀, under the mean spherical approximations. The results are in better agreement with experimental values. Presented at the 70th Indian Science Congress, Tirupathi, January 3–8, 1983.     

Perturbation theory for relativistic Lee model

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.     

Perturbation theory for QED bound states

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.     

Perturbation theory for two-dimensional gauge models

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.     

Perturbation theory in a framework of iteration methods

In a previous paper [J. Phys. A 36 (2003) 11807], we introduced the ‘asymptotic iteration method’ for solving second-order homogeneous linear differential equations. In this Letter, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem.     

H-theorem for a linear kinetic theory

A strongH-theorem is proved for the approximate linear kinetic theory of Bawzdziewicz and Cichocki, obtained by truncating a transformed hierarchy of evolution equations. For an ith truncation we define an entropy functional that is strictly increasing in time, unless the ith reduced distribution function depends on position coordinates only. It also follows that the only stationary solution of the linear kinetic theory is the equilibrium solution. In addition, we show that the usual symmetry properties of equilibrium time correlation functions are preserved by the approximate kinetic theory under consideration.On leave of absence from Institute of Physics, Szczecin University, Wielkopolska 15, Szczecin, Poland.     

Perturbation theory for large coupling constants

The perturbation technique for large coupling constantsg ² is used for obtaining the solutions of Schrödinger equation for a double exponential potential. In particular the solution valid forg ² e ^-r/2 g²e^-r/2 ? 1, is obtained int erms of confluent hypergeometric functions. A noteworthy aspect of this application is that the procedure developed can also be used for solving certain singular potentials.