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[en] We study the relations between the Caldirola-Kanai (C-K) description of friction in quantum mechanics and the fundamental master equation (ME) approach. The original C-K equation is shown to be equivalent to a ME without fluctuation term. In the case of the dampled haromic oscillator, the C-K equation with stochastic potential turns out to be equivalent to the complete ME. The formulation in terms of Wigner function is also worked out. (orig.)

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Physica A; ISSN 0378-4371; ; v. 116(1/2); p. 248-264

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[en] A paper of Boiti et al. concerning a 2-Kink solution of the Schroedinger equation is commented. (C.P.)

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[en] In this paper a survey is given of new results of the Painleve test and nonlinear evolution equations where ordinary- and partial-differential equations are considered. The authors study the semiclassical Haynes-Cumming model, the energy-eigenvalue-level-motion equation, the Kadomtsev-Petviashvili equation, the nonlinear Klein-Gordon equation and the self-dual Yang-Mills equation

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[en] Using our classification of separable Schroedinger equations with two space dimensions published in J. Math. Phys. 36, 5506 (1995) we give an exhaustive description of the coordinate systems providing their separability. Furthermore, we apply these results to separate variables in the heat, Hamilton endash Jacobi, and Fokker endash Planck equations. copyright 1997 American Institute of Physics

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AbstractAbstract

[en] We give a short proof of the semiclassical estimate for boundary values of resolvents of long range Schroedinger operators obtained by Robert and Tamura. Our proof is based on Mourre's commutator method and on the construction of a global escape function for the associated classical flow

[fr]

Dans cette Note nous donnons une nouvelle preuve de l'estimation semiclassique obtenue par Robert et Tamura pour des operateurs de Schroedinger a longue portee. La preuve utilise la methode des commutateurs de Mourre et la construction d'une fonction fuite globale pour le flot classique associeOriginal Title

Principe d'absorption limite pour des operateurs de Schroedinger a longue portee

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Comptes Rendus de l'Academie des Sciences. Serie 1; ISSN 0764-4442; ; CODEN CASME; v. 306(3); p. 121-123

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Brito, V.P.; Coelho, H.T.; Das, T.K.

International Union of Pure and Applied Physics

International Union of Pure and Applied Physics

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[en] Published in summary form only

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1989; 1 p; International Nuclear Physics Conference; Sao Paulo, SP (Brazil); 20-26 Aug 1989

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Miscellaneous

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AbstractAbstract

[en] First-order partial differential equations are solved which do not satisfy integrability conditions. Important examples of such equations in mathematical physics are the Liouville, the Dirac, the Vlasov equations etc. The set of boundary functions together with the vector field components, usub(i)(x), i = 4, 5, 6, determine the manifold, X

_{6}, which gives the support of the distribution function. The solution is presented here for the case of the Vlasov equation. The main result in this paper is eq. (9). The proof of construction is not given here. This method can be used to study also stability problems. The nonexistence of integrability conditions manifests itself by the reduction of R^{7}to the manifold X_{6}in which the solution exists. The method of constructing the solution is based on a new property of the PfaffiansPrimary Subject

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AbstractAbstract

[en] During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials

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Communications in Partial Differential Equations; ISSN 0360-5302; ; CODEN CPDIDZ; v. 18(1-2); p. 83-124

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AbstractAbstract

[en] The general scheme established in the previous paper for the efficient use of piecewise analytical perturbation series (PAPS) methods to solve linear ordinary differential equations is applied to the radial Schroedinger equation. Starting with a step function approximation to the potential, four optimal PAPS algorithms are written down which show orders of accuracy equal respectively to two, four, six and eight. A comparison with previously published methods in this class illustrates the importance of the optimal choice of the various parameters which enter the PAPS algorithms (approximation of the potential, keeping into the algorithm relevant terms only, adequate definition of the finite basis set of functions in terms of which the algorithms is expressed). A comparison with the Numerov method in its summed from (which is the most stable version with respect to round off) illustrates the significantly better performances of the optimal sixth order PAPS algorithns. (author)

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Dec 1984; 44 p

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[en] The piecewise analytical perturbation series (PAPS) approach to the solution of linear ordinary differential equations is shown to provide both PAPS algorithms and equations for the accumulated discretization errors, each of which involving the same set of propagators, a property which is very important for the implementation of PAPS codes with global control over the discretization error. Finite, simple and flexible PAPS algorithms can be derived provided the coefficients of the given differential equation are approximated by trucated piecewise Legendre series. Theoretical realization of such algorithms are outlined and their orders of accuracy are established

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Dec 1984; 44 p

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