A Complete Set of Functions in the Quantum Mechanical Three-body Problem PDF Download
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Author: Julia Nyiri
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Author: Julia Nyiri
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Author: Erich W. Schmid
Publisher: Elsevier
ISBN: 1483160785
Category : Science
Languages : en
Pages : 226
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The Quantum Mechanical Three-Body Problem deals with the three-body problem in quantum mechanics. Topics include the two- and three-particle problem, the Faddeev equations and their solution, separable potentials, and variational methods. This book has eight chapters; the first of which introduces the reader to the quantum mechanical three-body problem, its difficulties, and its importance in nuclear physics. Scattering experiments with three-particle breakup are presented. Attention then turns to some concepts of quantum mechanics, with emphasis on two-particle scattering and the Hamiltonian for three particles. The chapters that follow are devoted to the Faddeev equations, including those for scattering states and transition operators, and how such equations can be solved in practice. The solution of the Faddeev equations for separable potentials and local potentials is presented, along with the use of Padé approximation to solve the Faddeev equations. This book concludes with an appraisal of variational methods for bound states, elastic and rearrangement scattering, and the breakup reaction. A promising variational method for solving the Faddeev equations is described. This book will be of value to students interested in three-particle physics and to experimentalists who want to understand better how the theoretical data are derived.
Author: Leonard Eyges
Publisher:
ISBN:
Category : Quantum theory
Languages : en
Pages : 14
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Author: Leonard Eyges
Publisher:
ISBN:
Category : Integral equations
Languages : en
Pages : 18
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The quantum-mechanical ground-state problem for three identical particles bound by attractive inter-particle potentials is discussed. For this problem it has previously been shown that it is advantageous to write the wave function in a special functional form, form which an integral equation which is equivalent to the Schrodinger equation was derived. In this paper a new method for solving this equation is presented. The method involves an expansion of a two-body problem with a potential of the same shape as the inter-particle potential in the three-body problem, but of enhanced strength.
Author: John R. Jasperse
Publisher:
ISBN:
Category : Energy levels (Quantum mechanics)
Languages : en
Pages : 100
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A technique is presented for treating a general type of three-body bound-state problem for situations where the interaction may be written as the sum of three pair potentials. The method is based on the work of Eyges and consists of writing the total wavefunction for the three-body problem in a special form. Some simple one-dimensional applications are examined. The first involves delta-function pair-potentials including an example where one of the pair interactions is repulsive. The second involves the one-dimensional problem of three identical spinless particles interacting through attractive, square-well potentials. The helium atom is discussed from a three-body point of view. Each orbital is expanded into a complete set of two-body Sturmian functions for the Coulomb potential. For states in atomic helium of the form L=0 the equations assume a simplified form. For these states, the infinite set of integral equations generated by the expansion is truncated at several orders and solved numerically. Rapid convergence is demonstrated for low-lying states of the helium-like atoms using this method. In particular, results are reported for the 1s1s(1)S, 1s2s(1)S, and 2s2s(1)S states of He, Li(+), and H( - ).
Author: Misha Shifman
Publisher: World Scientific
ISBN: 9814436585
Category : Science
Languages : en
Pages : 560
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This invaluable collection of memoirs and reviews on scientific activities of the most prominent theoretical physicists belonging to the Landau School — Landau, Migdal, Zeldovich, Smorodinsky, Ter-Martirosyan, Kirzhnits, Gribov, Larkin and Anselm — are being published in English for the first time.The main goal is to acquaint readers with the life and work of outstanding Soviet physicists who, to a large extent, shaped theoretical physics in the 1950s-70s. Many intriguing details have remained unknown beyond the “Iron Curtain” which was dismantled only with the fall of the USSR.
Author:
Publisher:
ISBN:
Category : Three-body problem
Languages : en
Pages :
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Abstract: We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an approximation to the underlying physics, leading to an effective field theory. A method for perturbatively expanding the three-body bound-state equation in inverse powers of the cutoff is developed. This allows us to extract some analytical results concerning the behavior of the system. Further results are obtained by solving the leading order equations numerically to 11 or 12 digits of accuracy. The limit-cycle behavior of the required three-body contact interaction is computed, and the cutoff-independence of bound-state energies is shown. By studying the relationship between the two- and three-body binding energies, we obtain a high accuracy numerical calculation of Efimov's universal function. Equations for the first order corrections, necessary for the study of cutoff dependence, are derived. However, a numerical solution of these equations is not attempted.
Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 1288
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Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 1036
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Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 310
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