scholarly journals Dirac’s reduced radial equations and the problem of additional solutions

2017 ◽  
Vol 26 (07) ◽  
pp. 1750043 ◽  
Author(s):  
Anzor Khelashvili ◽  
Teimuraz Nadareishvili
Keyword(s):  
Boundary Condition ◽  
Quantum Mechanics ◽  
Dirac Equation ◽  
Radial Function ◽  
Delta Function ◽  
Two Dimensional ◽  
Radial Equation ◽  
Reduced Equations ◽  
Klein Gordon ◽  
History Of

We show that additional solutions must be ignored (in differences of the Schrödinger and Klein–Gordon equations) in the Dirac equation, where usually the second-order radial equation is passed, called the reduced equation, instead of a system. Analogously to the Schrödinger equation, in this process, the Dirac’s delta function appears, which was unnoted during the full history of quantum mechanics. This unphysical term we remove by a boundary condition at the origin. However, the distribution theory imposes on the radial function strong restriction and by this reason practically for all potentials, even regular, use of these reduced equations is not permissible. At the end, we include consideration in the framework of two-dimensional Dirac equation. We show that even here the additional solution does not survive as a result of usual physical requirements.

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

Towards a Relativistic Quantum Mechanics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Limit ◽  
Probability Current ◽  
Klein Gordon ◽  
Relativistic Equations

Towards a relativistic quantum mechanics. Klein–Gordon and the problems of the probability current and the negative energy solutions. The Dirac equation and negative energies. P, C, and T symmetries. Positrons. The Schrödinger equation as the non-relativistic limit of relativistic equations. Majorana and Weyl equations. Relativistic corrections in hydrogen-like atoms. The Dirac equation as a quantum system with an infinite number of degrees of freedom.

scholarly journals The Modified Fundamental Equations of Quantum Mechanics in Symmetric Forms

2021 ◽  
Author(s):  
Huai-Yu Wang
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Kinetic Energy ◽  
Time Derivative ◽  
Dinger Equation ◽  
Calculated Density ◽  
One Dimensional ◽  
Klein Gordon ◽  
Fundamental Equations ◽  
First Time

Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

Introduction

2017 ◽  
Author(s):  
Henk W. de Regt
Keyword(s):  
Quantum Mechanics ◽  
History Of Science ◽  
Crucial Role ◽  
Scientific Understanding ◽  
Related Question ◽  
History Of ◽  
Human Desire ◽  
Exciting Project ◽  
Understanding Science ◽  
The Way

This chapter introduces the theme of the book: scientific understanding. Science is arguably the most successful product of the human desire for understanding. Reflection on the nature of scientific understanding is an important and exciting project for philosophers of science, as well as for scientists and interested laypeople. As a first illustration of this, the chapter sketches an episode from the history of science in which discussions about understanding played a crucial role: the genesis of quantum mechanics in the 1920s, and the heated debates about the intelligibility of this theory and the related question of whether it can provide understanding. This case shows that standards of intelligibility of scientists can vary strongly. Furthermore, the chapter outlines and defends the way in which this study approaches its subject, differing essentially from mainstream philosophical discussions of explanatory understanding. It concludes with an overview of the contents of the book.

scholarly journals How Should We Categorize Approaches to the History of Political Thought?

2020 ◽  
Vol 83 (1) ◽  
pp. 91-114
Author(s):  
Adrian Blau
Keyword(s):  
Theoretical Analysis ◽  
Political Theory ◽  
Political Thought ◽  
Two Dimensional ◽  
History Of Political Thought ◽  
One Dimensional ◽  
History Of ◽  
New Framework

AbstractThis paper proposes a new framework for categorizing approaches to the history of political thought. Previous categorizations exclude much research; political theory, if included, is often caricatured. And previous categorizations are one-dimensional, presenting different approaches as alternatives. My framework is two-dimensional, distinguishing six kinds of end (two empirical, four theoretical) and six kinds of means. Importantly, these choices are not alternatives: studies may have more than one end and typically use several means. Studies with different ends often use some of the same means. And all studies straddle the supposed empirical/theoretical “divide.” Quentin Skinner himself expertly combines empirical and theoretical analysis—yet the latter is often overlooked, not least because of Skinner's own methodological pronouncements. This highlights a curious disjuncture in methodological writings, between what they say we do, and what we should do. What we should do is much broader than existing categorizations imply.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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