Analytic structure of the S-matrix for singular quantum mechanics

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.Fil: Camblong, Horacio E.. University of San Francisco; Estados UnidosFil: Epele, Luis Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; ArgentinaFil: Fanchiotti, Huner. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; ArgentinaFil: García Canal, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física. Laboratorio de Física Teórica; Argentin

Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions

Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical box of radius R. With the aid of the asymptotic iteration method, the exact analytic solutions under certain constraints, and general approximate solutions, are obtained. These exhibit the parametric dependence of the eigenenergies on a, b, and R. The wave functions have the simple form of a product of a power function, an exponential function, and a polynomial. In order to achieve our results the question of determining the polynomial solutions of the second-order differential equation (\sum_{i=0}^{k+2}a_{k+2,i}r^{k+2-i})y"+(\sum_{i=0}^{k+1}a_{k+1,i}r^{k+1-i})y'-(\sum_{i=0}^{k}\tau_{k,i}r^{k-i})y=0 for k=0,1,2 is solved.Comment: 16 pages, 1 figur

One-loop corrections of order (Z alpha)^6m_1/m_2, (Z alpha)^7 to the muonium fine structure

The corrections of order (Z alpha)^6m_1/m_2 and (Z alpha)^7 from one-loop two-photon exchange diagrams to the energy spectra of the hydrogenic atoms are calculated with the help of the Taylor expansion of corresponding integrands. The method of averaging the quasipotential over the wave functions in the d-dimensional coordinate space is formulated. The numerical values of the obtained contributions to the fine structure of muonium, hydrogen and positronium are presented.Comment: Talk given at the XVIth International Workshop High-Energy Physics and Quantum Field Theory (QFTHEP2001), Moscow, Russia, 6-12 Sep 2001, 12 pages, REVTE

Black-hole concept of a point-like nucleus with supercritical charge

The Dirac equation for an electron in the central Coulomb field of a point-like nucleus with the charge greater than 137 is considered. This singular problem, to which the fall-down onto the centre is inherent, is addressed using a new approach, based on a black-hole concept of the singular centre and capable of producing cut-off-free results. To this end the Dirac equation is presented as a generalized eigenvalue boundary problem of a self-adjoint operator. The eigenfunctions make complete sets, orthogonal with a singular measure, and describe particles, asymptotically free and delta-function-normalizable both at infinity and near the singular centre $r=0$. The barrier transmission coefficient for these particles responsible for the effects of electron absorption and spontaneous electron-positron pair production is found analytically as a function of electron energy and charge of the nucleus. The singular threshold behaviour of the corresponding amplitudes substitutes for the resonance behaviour, typical of the conventional theory, which appeals to a finite-size nucleus.Comment: 22 pages, 5 figures, LATEX requires IOPAR

High orders of the perturbation theory for hydrogen atom in magnetic field

The states of hydrogen atom with principal quantum number $n\le3$ and zero magnetic quantum number in constant homogeneous magnetic field ${\cal H}$ are considered. The coefficients of energy eigenvalues expansion up to 75th order in powers of ${\cal H}^2$ are obtained for these states. The series for energy eigenvalues and wave functions are summed up to ${\cal H}$ values of the order of atomic magnetic field. The calculations are based on generalization of the moment method, which may be used in other cases of the hydrogen atom perturbation by a polynomial in coordinates potential.Comment: 16 pages, LaTeX, 6 figures (ps, eps

Self-adjoint extensions and spectral analysis in Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $\alpha x^{-2}$. Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some "paradoxes" inherent in the "naive" quantum-mechanical treatment. We study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In addition, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.Comment: 39 page

Lie-algebraic interpretation of the maximal superintegrability and exact solvability of the Coulomb-Rosochatius potential in n dimensions

The potential group method is applied to the n-dimensional Coulomb-Rosochatius potential, whose bound states and scattering states are worked out in detail. As far as scattering is concerned, the S-matrix elements are computed by the method of intertwining operators and an integral representation is obtained for the scattering amplitude. It is shown that the maximal superintegrability of the system is due to the underlying potential group and that the 2n-1 constants of motion are related to Casimir operators of subgroups.Comment: 14 pages, 1 figure, to appear in J. Phys. A : Math. Theo

Renormalization of the Inverse Square Potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page

ВИЧ-инфекция и туберкулез с множественной лекарственной устойчивостью: частота сочетания, эффективность лечения

The objective of the study: in Tomsk Region, to establish the frequency of multiple drug resistance (MDR) of mycobacterium tuberculosis (MBT) in new tuberculosis patients with the reference to their HIV status and to assess their treatment outcomes.Subjects and methods. The presented results were obtained from a retrospective cohort study of 788 new tuberculosis patients who were registered for MDR TB treatment at Tomsk Phthisiopulmonology Medical Center from January 2017 to April 2019.Results. In Tomsk Region, the level of primary MDR reaches 31.3% in patients with TB/HIV co-infection, while in HIV negative tuberculosis patients, this rate is 24.2%. The incidence of primary MDR/XDR MTB reaches 40% among deceased patients with TB/HIV co-infection. Treatment efficacy in MDR/XDR TB patients with associated HIV infection is low – the effective treatment was achieved only in 7.3% of them. In general (excluding the data on MTB drug resistance and antiretroviral therapy), treatment efficacy of tuberculosis patients with HIV infection is significantly lower versus HIV negative tuberculosis patients: 37.7% and 61.9%, respectively, OR 0.38 [0.28; 0.50], p = 0.001.Цель исследования: установить частоту встречаемости множественной лекарственной устойчивости (МЛУ) микобактерий туберкулеза (МБТ) у впервые выявленных больных туберкулезом в зависимости от ВИЧ-статуса на территории Томской области, оценить исходы их лечения.Материалы и методы. Представленные результаты получены на основе ретроспективного когортного исследования 788 больных впервые выявленным туберкулезом органов дыхания, которые были зарегистрированы для лечения МЛУ-туберкулеза в ОГАУЗ «Томский фтизиопульмонологический медицинский центр», в период с января 2017 г. по апрель 2019 г.Результаты. В Томской области уровень первичной МЛУ МБТ достигает 31,3% у больных туберкулезом в сочетании с ВИЧ-инфекцией, у пациентов с туберкулезом и ВИЧ-негативным статусом этот показатель ‒ 24,2%. Частота первичной МЛУ/ШЛУ МБТ достигает 40% среди умерших пациентов с туберкулезом и ВИЧ-инфекцией. Эффективность лечения пациентов с МЛУ/ШЛУ-туберкулезом на фоне ВИЧ-инфекции низкая ‒ эффективный курс достигнут только у 7,3% больных. В целом (без учета данных о лекарственной устойчивости МБТ и приема антиретровирусной терапии) эффективность лечения больных туберкулезом с ВИЧ-инфекцией значительно ниже, чем больных туберкулезом с негативным ВИЧ-статусом: 37,7 и 61,9% соответственно, ОШ 0,38 [0,28; 0,50], p = 0,001