The Magnetic Vector Potential, Klein-Gordon Equation and Klein's Paradox in Relativistic Quantum Mec

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The Magnetic Vector Potential, Klein-Gordon Equation and Klein's Paradox in Relativistic Quantum Mechanics

Author : David L. Schaffer

Publisher : Wichita State University, College of Liberal Arts and Sciences, Department of Physics

Published : 2007

ISBN-10 :

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Number of Pages : 648 Pages

Language : en

Descriptions The Magnetic Vector Potential, Klein-Gordon Equation and Klein's Paradox in Relativistic Quantum Mechanics

[Author abstract] This Thesis evaluates solutions to the Klein-Gordon equation with scalar and vector potentials in the ymmetric and Landau gauges. The solution for the Klein-Gordon equation in the Symmetric gauge does reproduce elements of the two dimensional quantum harmonic oscillator. The Landau gauge solution is used in the velocity selector situation where particles can have acceleration free motion for a selected velocity. The Klein paradox for spinless particles is reviewed and its application to the Klein-Gordon equation shows that the vector potential can have an effect on particle pair production without the violation of conservation of momentum or energy, that this effect is to suppress the particle pair production associated with Klein's paradox and that the suppressive effect can, under certain conditions, become strong enough to prevent particle pair production in Klein's paradox when the scalar potential is otherwise many times what would be necessary to create Klein's paradox particle pairs.

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Results The Magnetic Vector Potential, Klein-Gordon Equation and Klein's Paradox in Relativistic Quantum Mechanics

3: The Schrödinger Equation and a Particle in a Box - 3.E: The Schrödinger Equation and a Particle in a Box (Exercises) These are homework exercises to accompany Chapter 3 of McQuarrie and Simon's "Physical Chemistry: A Molecular Approach" Textmap. Thumbnail: The quantum wavefunction of a particle in a 2D infinite potential well of dimensions L x and L y. The wavenumbers are n x = 2 and n y = 2

1.1 The Scope and Scale of Physics - OpenStax - Figure 1.3 (a) Using a scanning tunneling microscope, scientists can see the individual atoms (diameters around 10 -10 m) that compose this sheet of gold. (b) Tiny phytoplankton swim among crystals of ice in the Antarctic Sea. They range from a few micrometers (1 μm is 10 -6 m) to as much as 2 mm (1 mm is 10 -3 m) in length. (c) These two colliding galaxies, known as NGC 4676A (right

(PDF) Classes of exact Klein-Gordon equations with spatially dependent - Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential . × Close Log In. Log in with Facebook Log in with Google. or. Email. Password. Remember me on this computer. or reset password. Enter the email address you signed up with and we'll email you a reset link

Solutions of Klein-Gordon equation with Mie-type potential via the - A study is undertaken to derive the exact solutions of the Klein-Gordon with the Mie-type potential in the presence of the nonzero space component of a vector potential field. The wave functions and the energy spectrum are derived via the Laplace transformation method and by assuming equal scalar and time component of the vector potential. The Mie-type potential describes four different

Klein-Gordon equation - Wikipedia - The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is a relativistic wave equation, related to the Schrödinger is second-order in space and time and manifestly is a quantized version of the relativistic energy-momentum relation = + ().Its solutions include a quantum scalar or pseudoscalar field, a field

scalar and vector potentials On solution of Klein-Gordon equation in - expressed by equation (10 )can not be derived from equation (9) which is Klein-Gordon equation in static scalar and vector potential, equation (1) is incorrect. Moreover, some papers [2-27] which are so- called solution of Klein-Gordon equation in equal scalar and vector potentials are wrong too . References [1] W. Greiner, Relativistic Quantum

Ch. 1 Introduction - University Physics Volume 1 | OpenStax - 1.1 The Scope and Scale of Physics. 1.2 Units and Standards. 1.3 Unit Conversion. 1.4 Dimensional Analysis. 1.5 Estimates and Fermi Calculations. 1.6 Significant Figures. 1.7 Solving Problems in Physics. As noted in the figure caption, the chapter-opening image is of the Whirlpool Galaxy, which we examine in the first section of this chapter

Derivation of Klein-Gordon equation from Maxwell's ... - ResearchGate - The wave equation from that study has in turn been used to obtain the Klein-Gordon equation ... Built directly from the Maxwell's equations, the vector potential ... manent magnetic moment

The magnetic vector potential, Klein-Gordon equation and Klein's - Figure 10.2. The Vector Potential in the Landau Gauge A = Byx, where x is the unit vector in the x direction. - "The magnetic vector potential, Klein-Gordon equation and Klein's paradox in relativistic quantum mechanics"

Exact Solutions of the Klein-Gordon Equation with Hylleraas Potential - Enter the email address you signed up with and we'll email you a reset link

The magnetic vector potential, Klein-Gordon equation and Klein's - Corpus ID: 122782809; The magnetic vector potential, Klein-Gordon equation and Klein's paradox in relativistic quantum mechanics @inproceedingsSchaffer2007TheMV, title=The magnetic vector potential, Klein-Gordon equation and Klein's paradox in relativistic quantum mechanics, author=David L. Schaffer, year=2007

PDF Exact Solutions of the Klein-Gordon Equation in the Presence of ... - arXiv - The well known prescription adopted to introduce electromagnetic four-vector potential, A µ, in the Dirac and Klein-Gordon equations is by the minimal coupling one. By this prescription, the four-vector diﬀerential operator P µ = i∂ µ is modiﬁed as P µ −→ P µ − eA µ. Several years ago, Dosch, Jansen and Mu¨ller in [18

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A Notable Quasi-Relativistic Wave Equation and Its Relation to the - Journal of Modern Physics > Vol.12 No.8, June 2021

PDF Solutions of the Maxwell equations and photon wave functions - A possible advantage of using a vector potential is that it is the solution of a scalar wave equation, which has a well-known Green function. However, this advantage is oﬀset by the fact that we provide a covariant Green function for the Maxwell equation. This paper is organized as follows. In Sec. 2 the vector Maxwell equations and the Dirac

PDF The Magnetic Vector Potential, Klein-gordon Equation and Klein'S - THE MAGNETIC VECTOR POTENTIAL, KLEIN-GORDON EQUATION AND KLEIN'S PARADOX IN RELATIVISTIC QUANTUM MECHANICS A Thesis by David L. Schaffer Bachelor's Degree, University of Utah, 1982 Submitted to the Department of Physics and the faculty of the Graduate School of Wichita State University in partial fulfillment of

Magnetic vector potential - Wikipedia - In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: =.Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently

Solution of the Klein-Gordon for exponential scalar and vector - In this Letter we introduce the exponential potential and get bound state solutions of the s-wave Klein-Gordon equation when the scalar potential is greater than the vector potential. It is important that this wave equation is equal to the s-wave Schrödinger equation with Klein-Gordon-Morse potential. This Letter is organized as follows

Bound states of the Klein-Gordon equation with vector and scalar Rosen - Solving Klein-Gordon equation with equal scalar and vector Rosen-Morse-type potentials, we obtain the exact energy equation for the s-wave bound states. It has been shown that the energy equations and corresponding wavefunctions for the standard Rosen-Morse well, Eckart potential and their PT-symmetric versions are included in those for

Effective Mass Klein-gordon Equation With Position Dependent Magnetic Field - The s-wave Klein-Gordon equation, with position-dependent mass, is solved for the exponential vector and scalar potentials by an alternative approach. The asymptotic iteration method is used to

The magnetic vector potential, Klein-Gordon equation and Klein's - The Klein Paradox for spin less particles is reviewed and its application to the Klein- Gordon equation shows that the vector potential can have an effect on particle pair production without the violation of conservation of momentum or energy, that this effect is to suppress the particle pair production associated with Klein's paradox and

THE MAGNETIC VECTOR POTENTIAL, KLEIN-GORDON EQUATION AND - THE MAGNETIC VECTOR POTENTIAL, KLEIN-GORDON EQUATION AND KLEIN’S PARADOX IN RELATIVISTIC QUANTUM MECHANICS A Thesis by David L. Schaffer Bachelor’s Degree, University of Utah, 1982 Submitted to the Department of Physics and the faculty of the Graduate School of Wichita State University in partial fulfillment of

scalar and vector potentials On solution of Klein-Gordon - The correct equation developed in this comment demonstrates that so-called the Klein-Gordon equation with scalar and vector potentials is incorrect; therefore, some papers published to solve Klein-Gordon equation with equal scalar and vector potential are also wrong

Klein–Gordon equation - Wikipedia - What is the Klein–Gordon equation?

Quantum Mechanics of Klein-Gordon equation - - to Klein-Gordon equation ( + m2c2 ~2)ψ(t,x) = 0 , (1.3) where = 1 c2∂ 2 t −∆ = ∂µ∂µ is the d’Alembert operator. From now on we will use the natural units c= ~= 1, furthermore we can denote K= −∆ + m2 and rewrite (1.3) as (i∂t)2ψ(t,x) = Kψ(t,x) . (1.4) Unlike Schro¨dinger equation, the free Klein-Gordon equation is invariant

Bound states of the Klein–Gordon equation with vector and - According to Ref. , the s-wave Klein–Gordon equation with scalar and vector potentials is (ℏ = c = 1) (1) d 2 d r 2 + [E − V (r)] 2 − [M + S (r)] 2 u (r) = 0, where E denotes the energy, M denotes the mass, and the radial wave function is R (r) = u (r) / r

The magnetic vector potential, Klein-Gordon equation and - The solution for the Klein-Gordon equation in the Symmetric gauge does reproduce elements of the two dimensional quantum harmonic oscillator. The Landau gauge solution is used in the velocity selector situation where particles can have acceleration free motion for a selected velocity

Klein–Gordon equation - Wikipedia - The Klein–Gordon equation was first considered as a quantum wave equation by Schrödinger in his search for an equation describing de Broglie waves. The equation is found in his notebooks from late 1925, and he appears to have prepared a manuscript applying it to the hydrogen atom