One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.Comment: 10 pages, 1 figur

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page

One dimensional Coulomb-like problem in deformed space with minimal length

Spectrum and eigenfunctions in the momentum representation for 1D Coulomb potential with deformed Heisenberg algebra leading to minimal length are found exactly. It is shown that correction due to the deformation is proportional to square root of the deformation parameter. We obtain the same spectrum using Bohr-Sommerfeld quantization condition.Comment: 11 pages, typos corrected, references adde

WKB approximation in deformed space with minimal length

The WKB approximation for deformed space with minimal length is considered. The Bohr-Sommerfeld quantization rule is obtained. A new interesting feature in presence of deformation is that the WKB approximation is valid for intermediate quantum numbers and can be invalid for small as well as very large quantum numbers. The correctness of the rule is verified by comparing obtained results with exact expressions for corresponding spectra.Comment: 13 pages Now it is avaible at http://stacks.iop.org/0305-4470/39/37

Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction

For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $\delta$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-body problem, exact bosonizationComment: 4 pages ReVTeX 4 epsf figures included, new Ref

Charged particle in the field an electric quadrupole in two dimensions

We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support a tridiagonal matrix representation for the angular and radial components of the wave operator. This solution is for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations. The charged particle could become bound to the quadrupole only if its moment exceeds a certain critical value.Comment: 16 pages, 2 Tables, 4 Figure

Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

ASSESSMENT OF OCCURRENCE OF ASYMMETRY OF FOLIDOZ OF THE HEAD AT ORDINARY (NATRIX NATRIX LINNAEUS, 1758) AND WATER (NATRIX TESSELLATA LAURENTI, 1768) UZHEY IN ANTHROPOGENE-MODIFIED AND NATURAL LANDSCAPES OF THE VOLGOGRAD REGION

The real work represents the analysis of frequency of occurrence of asymmetry of bilateral structures of a scaly cover of ordinary and water ears in the territory of the Volgograd region in the anthropogene-modified and natural landscapes, based on original these authors. Manifestation of asymmetry of a folidoz of the head of these types most possibly in number of labial, supralabial and temporal guards. Close indicators of coefficients of asymmetry of different types of the sort Natrix tells about similarity of microclimatic conditions and influence of factors of destabilization of ontogenetic development.Настоящая работа представляет собой анализ частоты встречаемости асимметрии билатеральных структур чешуйчатого покрова обыкновенного и водяного ужей на территории Волгоградской области в антропогенно-модифицированных и естественных ландшафтах, основанный на оригинальных данных авторов

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Создание новой формы метронидазола и ее клиническое применение в схемах комплексного лечения больных раком прямой кишки

A review of russian and foreign literature concerning clinical use of metronidazole as a radiosensitizer in oncologic treatment. New delivery form of metronidazole has been developed using a polymeric composition. Dose- and time-dependent pharmacodynamics has been analyzed. Personal long-term results of complex treatment of localized and locally-advanced rectal cancer using different radiosensitizers has been presented. The data allows to consider complex treatment as a method of choice for these patients. Using polyradiomodification allowed to decrease lymphohematogenic metastasing rate, decrease locoregional recurrence rate and improve disease-free survival.В статье представлен обзор отечественной и зарубежной литературы, посвященной клиническому использованию радиомодификатора — метронидазола (МЗ) в лечении онкологических больных. Создана новая форма МЗ в составе полимерной композициии представлен анализ его фармакодинамики в опухоли в зависимости от концентрации его в полимерной композиции и времени нахождения полимерной композиции в прямой кишке. Представлены собственные многолетние результаты хирургического, комбинированного и комплексного методов лечения операбельного и местно-распространенного рака прямой кишки (РПК) с использованием различных радиомодификаторов. Полученные данные позволяют считать комплексный метод лечения РПК методом выбора. Реализация программы полирадиомодификации позволила снизить частоту лимфогематогенного метастазирования, существенно снизить развитие локорегионарных рецидивов и значительно улучшить показатели безрецидивной выживаемости больных