A general iterative time-independent perturbation theory

1985 ◽  
Vol 63 (9) ◽  
pp. 1157-1161 ◽  
Author(s):  
F. Castaño ◽  
L. Laín ◽  
M. N. Sanchez ◽  
A. Torre
Keyword(s):  
Perturbation Theory ◽  
Power Series ◽  
Iterative Method ◽  
Perturbation Methods ◽  
Lennard Jones ◽  
Insight Into ◽  
Considerable Insight

An iterative method for time-independent perturbation theory is presented. Lennard-Jones–Brillouin–Wigner (LBW) and Rayleigh–Schrödinger (RS) power series are shown to be particular cases of the iteration and the combined expansion–iteration. Improvements in convergence of the power series are suggested and analyzed.The iterative method gives considerable insight into the nature and relative convergence of the currently used time-independent perturbation methods.

A perturbation calculation of properties of the helium iso-electronic sequence

1958 ◽  
Vol 247 (1249) ◽  
pp. 245-259 ◽  
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Power Series ◽  
Perturbation Methods ◽  
Ground States ◽  
Radiative Corrections ◽  
Perturbation Calculation ◽  
Magnetic Susceptibilities ◽  
Dipole Polarizabilities

Perturbation methods are employed to calculate the magnetic susceptibilities and the dipole polarizabilities of the ground states of the members of the helium iso-electronic sequences and also the mass polarization, relativistic and radiative corrections to their energies, the results being obtained as power series in the inverse of the nuclear charges. The calculations are prefaced by a brief résumé of the equations of perturbation theory applicable to the case when the unperturbed wave function is known only approximately.

scholarly journals Characterisations in Britain of Isaac Newton’s Approach to Physical Inquiry in the Principia between 1687 and 1713

2021 ◽  
Vol 26 (4) ◽  
pp. 341-372
Author(s):  
Jip van Besouw ◽  
Steffen Ducheyne
Keyword(s):  
Historical Record ◽  
Public Perceptions ◽  
Philosophical Approach ◽  
The Impact ◽  
Insight Into ◽  
Considerable Insight

Abstract In order to gain a better understanding of the impact and circulation of the first edition of the Principia, we offer an analysis of public perceptions in Britain of Isaac Newton’s approach to physical inquiry in the Principia between the appearance of its first and second editions, in 1687 and 1713, respectively. We treat Newton’s readers as actors with distinctive scholarly backgrounds and interests rather than as followers or popularisers of a “Newtonian philosophy,” a label we find to be largely absent in the historical record before 1713, when it was purposefully used by Roger Cotes in his preface to the second edition of the Principia. Through our survey, we gain considerable insight into how Newton’s readers characterised the Principia and its author. We establish that British readers of the first edition of the Principia ascribed a relatively stable and interrelated number of characteristics to Newton’s natural philosophical approach, although different readers emphasised different things. We also show that the most detailed accounts of Newton’s natural philosophical approach were, not surprisingly, given in polemical contexts. We find that it is only at the very end of this period, and in polemical contexts, that the notion of a “Newtonian philosophy” with a specific and pathbreaking approach to physical inquiry arose.

Aspects of the weak-coupling theory of open systems

1983 ◽  
Vol 61 (11) ◽  
pp. 1479-1485 ◽  
Author(s):  
I. D. Cox ◽  
W. E. Hagston ◽  
B. J. Holmes
Keyword(s):  
Perturbation Theory ◽  
Open System ◽  
Weak Coupling ◽  
Open Systems ◽  
Higher Order ◽  
Projection Operators ◽  
Coupling Theory ◽  
Weak Coupling Theory ◽  
Damping Theory ◽  
Insight Into

Damping theory of an open system S is usually formulated in terms of projection operators which introduce nonuniqueness into the analysis. An insight into the nature of the approximations that arise from this aspect of the formalism is revealed by considering systems of varying complexity. This leads to the conclusion that the results of higher order perturbation theory approximations may not be meaningful.

A Uniform Method for Determining Angular Accelerations in Mechanisms

1946 ◽  
Vol 13 (1) ◽  
pp. A41-A44
Author(s):  
L. R. Koenig
Keyword(s):  
Full Advantage ◽  
Velocity Vector ◽  
Angular Acceleration ◽  
Uniform Method ◽  
Insight Into ◽  
Considerable Insight

Abstract The purpose of this paper is to disclose a more reliable and uniform method, applicable to mechanisms in general, for determining directly the angular accelerations of the constituent links. The method completely suffices where the determination of angular accelerations is the end in view. Although it is independent of normal, tangential, and total accelerations of points on the links, reliable determinations of such accelerations are considerably facilitated with the aid of the acquired angular accelerations. Angular-acceleration problems may be solved with increased assurance because; (a) only velocity-vector considerations are required in the necessary kinematic layouts; (b) full advantage may be taken of the process of inversion in simplifying velocity-vector layouts, which is not possible when acceleration vectors are employed; and (c) the method gives considerable insight into the effects of the various factors controlling the angular accelerations.

Remembrances

Tallis ◽  
2020 ◽  
pp. 197-208
Author(s):  
Kerry McCarthy
Keyword(s):  
Family Background ◽  
The Other ◽  
The Everyday ◽  
The Will ◽  
Insight Into ◽  
Considerable Insight

This final chapter returns to the details of Tallis’s biography. It examines his will and the will of his wife Joan, two documents which offer considerable insight into his social circles and the everyday material surroundings of his household, as well as what little we can deduce of his family background. The chapter also discusses Tallis’s epitaph (very recently rediscovered by the author in a more accurate version) and the other memorial poems written at his death in 1585, including Ye sacred Muses, set to music by Byrd. It concludes with some reflections on Tallis’s enigmatic life and his musical gifts.

Block-Finite Orthomodular Lattices

1979 ◽  
Vol 31 (5) ◽  
pp. 961-985 ◽  
Author(s):  
Günter Bruns
Keyword(s):  
Orthomodular Lattice ◽  
Boolean Algebras ◽  
Orthomodular Lattices ◽  
Special Situation ◽  
The Given ◽  
Insight Into ◽  
Considerable Insight

Introduction. Every orthomodular lattice (abbreviated : OML) is the union of its maximal Boolean subalgebras (blocks). The question thus arises how conversely Boolean algebras can be amalgamated in order to obtain an OML of which the given Boolean algebras are the blocks. This question we deal with in the present paper.The problem was first investigated by Greechie [6, 7, 8, 9]. His technique of pasting [6] will also play an important role in this paper. A case solved completely by Greechie [9] is the case that any two blocks intersect either in the bounds only or have the bounds, an atom and its complement in common. This is, of course, a very special situation. The more surprising it is that Greechie's methods, if skillfully applied, yield considerable insight into the structure of OMLs and provide a seemingly unexhaustible source for counter-examples.

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

2019 ◽  
Vol 118 (1) ◽  
pp. e1582813 ◽  
Author(s):  
Mostafa Abolala ◽  
Kiana Peyvandi ◽  
Farshad Varaminian ◽  
Seyed Majid Hashemianzadeh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Perturbation Theory ◽  
Thermodynamic Properties ◽  
Lennard Jones
Sign in / Sign up

Export Citation Format

Share Document