The dirac equation is more restrictive than the klein gordon equation. Generalized dirac and kleingordon equations for spinor. We establish local and global existence results for dirackleingordon equations in one space dimension, employing a null form estimate and a. The convergence of solutions of the dirac and kleingordon equations to solutions of the pauli and schrodinger equations in the nonrelativistic limit is discussed. In the present work, we like to study the cauchy problem for the. The form of the twobody dirac equations which most readily incorporates each or any number of these intereractions in concert is the socalled hyperbolic form of the tbde. Lorentz transformations the free particle kleingordon equation 10. We will solve these equations by means of a fourier expansion in modes of the form. This and some others problem drove dirac to think about another equation of motion. Pdf solutions for the kleingordon and dirac equations on. In case youd like to merge pdf files locally, download pdfmerge, install it then open programsneeviapdf and run pdfmerge.
Pdf a discrete scheme for the dirac and kleingordon. For combined scalar and vector interactions those forms ultimately reduce to the ones given in the first set of equations of this article. Inequivalence of kleingordon and dirac equation hans detlef hutten. The kleingordon equation in the spacetime representation 9 the quantity q2 is represented by the differential operator dalembert operator from the mass shell condition 6 this results in the kleingordon equation as the basic field equation of the scalar field. His starting point was to try to factorise the energy momentum relation. Pdf electromagnetic kleingordon and dirac equations in. All these interpretations are awkward and not easy to handle. The kleingordon equation kleinfockgordon equation or sometimes kleingordonfock equation is a relativistic wave equation, related to the schrodinger equation. Comparison among kleingordon equation, dirac equation and relativistic stationary schr. Gordon equation for this combined potential is exactly obtained by using a systematical solution method which is introduced by nikiforovuvarov nu. To handle this problem, dirac appealed to the fact that electrons are fermions and no two electrons could take the same quantum state the pauli exclusion principle. Chapter 11 em lorentz force derived from klein gordons equation from my book. But why did it need to be of first order in time and. Diracs the principles of quantum mechanics laurie m.
In physics, relativistic quantum mechanics rqm is any poincare covariant formulation of. Also we would like to have a consistent description of the spin of the electron that in the nonrelativistic theory has to be added by hand. This means that, if we merely combine the two covariances as done previously for the kleingordon equation when a nonzero spin particle is. Separation of variables and exact solution of the klein. Diracs book, the principles of quantum mechanics, summarized the foundations of a new science,much of which was his own creation. He wanted a relativistic solution so it makes sense that the solution needed to satisfy einsteins energymomentum relation. Mapping of the relativistic kinetic balance equations onto the kleingordon and secondorder dirac equations adriana i pesci 1, raymond e goldstein,2 and hermann uys 1 department of physics, university of arizona, tucson, az 85721, usa 2 program in applied mathematics, university of arizona, tucson, az 85721, usa. China weimin zhouy and jun yanz department of physics, new york university, 4 washington place, new york, ny, 3 a particle is always not pure. Dirac himself remarked in one of his talks that his equation was more intelligent than its author. Pdf electromagnetic kleingordon and dirac equations in scale. Regularity results for the dirackleingordon equations. The elementary solutions have a position dependence of the form eik. Relativistic quantum mechanics kleingordon equation dirac.
In section 3, we discuss the solutions of the massless dirac equations in this background and show how to recover the expression of the hawking temperature. Researcharticle heuntype solutions of the kleingordon and dirac equations in the garfinklehorowitzstrominger dilaton black hole background marinaauradariescu,1 cipriandariescu,1 andcristianstelea 2 facultyofphysics,alexandruioancuzauniversity,blvd. The solutions to the dirac equation are also solutions of the kleingordon equation, which is the equation of motion for the real scalar field. The dirac equation and the klein gordon kg equation are the most frequently used wave equations for the description of particle dynamics in relativistic quantum mechanics. Solutions for the kleingordon and dirac equations on the. Upload your pdf files, choose the order and download your merged pdf. Why do dirac spinors obey the kleingordon equation.
Bound states of the kleingordon and dirac equations for potential v r ar2br1. Comparison among kleingordon equation, dirac equation and. The plane waves 10 are basic solutions and the field 9 is constructed by. Components of dirac equation solve the klein gordan equation derivation. The dirackleingordon system dkg arises in the socalled yukawa interaction 3, and describes an interaction between a dirac spinor of mass m 0 and a meson eld of mass m 0. There is no need to install special software and uploaded files can be in various formats like doc, xls, ppt and so on. This approach was used also to derive the kleingordon equation. In its free form, or including electromagnetic interactions, it describes all spin 1. Kleingordon and dirac equations with thermodynamic quantities. Is the dirac equation equivalent to the kleingordon. Solutions of the kleingordon equation for the harmonic. A general solution of kgd equation as a superposition of two dirac plane harmonic waves with different masses has been obtained. Pdf merge free enables you to merge multiple pdf files in the simplest and fastest way. I can see that the converse is not true, but why do spinors follow the equation for realfield particles.
Solutions for the kleingordon and dirac equations on the lattice based on chebyshev polynomials article pdf available in complex analysis and operator theory 102. Klein gordon and dirac equations with positiondependent mass for. Separation of variables for the kleingordon and dirac. Dirac matrices are described as quaternion valued and the dirac hamiltonian is considered as hermitian with real eigenvalues of energy. Ppt relativistic qm the klein gordon equation 1926. Generalized kleingordon and dirac equations from nonlocal. Dirac equation derivation and introduction youtube. Find out more about this on our privacy policy page. We present a new step in the foundation of quantum field theory with the tools of scale relativity. The dirac and kleingordon equations with equal scalar and. Klein gordon equation that includes this dirac current probability. A large number of potentials have been constructed. A complex field remains a complex field as expected for nonrelativistic problems where we are all familiar with wave functions and their interpretation.
It is the purpose of the present article to solve the klein gordon and dirac equations in. Pdf candy provides you with a unique tool to merge pdf files and it is absolutely free for everyone. Ever since the invention of the kleingordon and dirac equations for the quantum mechanics of single particles, relativistic quantum mechanics. In the dirac case, the discrete solution converges to the continuum propagator and it can also be rewritten in the form. Dirac and kleingordon equations with equal scalar and. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist paul dirac in 1928. Multiply the nonconjugated dirac equation by the conjugated wave function from the left and multiply the conjugated equation by the wave function from right and subtract the equations.
Each element of the matrices in equations 34 are 2x2 matrices. It is a quantized version of the relativistic energymomentum relation. We compare the solutions and the energy spectra obtained with the corresponding ones from the dirac equation for a spin onehalf relativistic particle. We interpret this as an equation of continuity for probability with j.
Electromagnetic kleingordon and dirac equations in scale relativity article pdf available in international journal of modern physics a 2522 september 2010. The non relativistic limit of the klein gordon equation kg is the schrodinger equation s. What is the relationship between the dirac equation and. Dirac equation from the kleingordon one as for the free particle motion, i. The development of a welladapted discrete clifford calculus framework based on spinor fields allows us to represent, using solely projection based.
The kleingordon equation is a linear homogeneous secondorder partial differential equation with constant coefficients. Then press the merge button to get your merged pdf. He then tried to find solutions, but was dismayed to find that problems like nonpositivedefinite probability curre. Is the dirac equation equivalent to the kleingordon equation. Klein gordon and squareroot operator equations for twospinors and scalars. Comparison among kleingordon equation, dirac equation. The discovery of dirac equation and its impact on present. Pdf joiner allows you to merge multiple pdf documents and images into a single pdf file, free of charge.
For every solution to the dirac equation, its components will be a solution of the klein gordon equation, but the converse isnt true. And due to the interchange of space and time in the lorentz transformation, dirac was motivated to develop the equation with single spatial and temporal derivatives. To learn more, see our tips on writing great answers. It is the purpose of the present article to solve the kleingordon and dirac equations in.
Why is the klein gordon equation of second order in time. Dirac and kleingordon equations with equal scalar and vector potentials a. An abstract theory of these equations is developed which is general enough to allow physical space to be an arbitrary complete riemannian manifold. All uploaded files will be deleted permanently within 15 minutes. The dirac equation is invariant under charge conjugation, defined as changing electron states into the opposite charged positron states with the same momentum and spin and changing the sign of external fields. Nov 24, 2009 analytical solutions to the klein gordon equation with positiondependent mass for qparameter poschlteller potential. A generalized klein gordon equation with a closed system. Chapter 11 em lorentz force derived from klein gordons. Pdf analytical solutions to the kleingordon equation with. To get rid of this drawback, we combine otherwise the quantum and scale co. It should be added, however, that it was dirac who found most of the additional insights.
For every solution to the dirac equation, its components will be a solution of the kleingordon equation, but the converse isnt true. The dirac equation is one of the two factors, and is conventionally taken to be p m 0 31 making the standard substitution, p. The negative energy solutions, which were caused by the second derivative of time in the klein gordon equation, motivated dirac to develop an equation with a single derivative of time. Klein gordon equation dirac equation the hydrogen atom dirac equation with a central potential separation of the radial and angular components energy levels of the hydrogen atom patrick puppel dirac equation and hydrogen atom. Solutions of the timedependent kleingordon and dirac equations for a uniform electric field vernon w. The dirac equation we will try to find a relativistic quantum mechanical description of the electron. The conditions 7 are conveniently expressed in terms of anticommutators. Mapping of the relativistic kinetic balance equations onto. Kleingordon and squareroot operator equations for two. The dirac equation for a particle in a spherical box potential with application in bag modeling blomquist, emil. Pdf dirac and kleingordon equations in curved space. Relativistic quantum mechanics is developed, including the klein gordon equation and up to the dirac equation. Electromagnetic kleingordon and dirac equations in scale. The transmission coefficient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated.
Inequivalence of klein gordon and dirac equation hans detlef hutten bach abstract. The problems with the kleingordon equation led dirac to search for an alternative. To do this the dirac spinor is transformed according to. The kleingordon equation was of second order in time and it did not have a positive. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one and threedimensional box using the klein gordon equation in the feshbachvillars formalism.
Toobtain the dirac wave equation we use the factorizationof the secondorder invariant casimir operatorassociated to the fantappiede sitter group. Dirackleingordon equations in one space dimension yungfu fang abstract. The schrodinger equation is not relativistically invariant. Pdf we present a new step in the foundation of quantum field theory with the. The final formalism of dealing with the relativistic quantum equations has been developed since that time and is now called the quantum field theory. The discovery of dirac equation and its impact on presentday physics reproduced with permission from dirac cmd feynman.
The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of kleingordon and dirac equations for which chebyshev polynomials of the first kind may be used to represent a set of solutions. Pio neers in quantum mechanics, edited by ranabir dull and asim k ray, wiley eastern limited, 1993. In sections 3 and 4, we deal with the construction of potentials for the kleingordon and dirac equations respectively. Diracs solution to the kleingordon equation physics forums. Relativistic qm the klein gordon equation 1926 1 relativistic qm the klein gordon equation 1926 scalar particle field j0 energy eigenvalues 1927 dirac tried to eliminate negative solutions by writing a relativistic equation linear in e a theory of fermions 1934 pauli and weisskopf revived kg equation with. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scalecovariant derivative tool. Boththe kleingordon and dirac wave equations arediscussed in terms of the spherical harmonics with spinweight. The fact that these two equations, for free particles, are constructed using two objects. Dirac and kleingordon equations with equal scalar and vector.
Myers institute for materials research, national bureau of standards, washington, d. Gordon and dirac equations are obtained for a particle moving in an arbitrary plane electromagnetic wave in vacuo plus a uniform static magnetic field parallel to the direction of propagation of the electromagnetic wave. The klein gordon equation in the presence of a spatially onedimensional hulthen potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. All the files you upload as well as merged pdf will be deleted permanently within a few minutes. The kleingordon equation is applied in the description of mesons and corresponding fields. The timedependent kleingordon and dirac equations are solved for the motion of a charged particle in a classical uniform electrostatic field of infinite extent. Moreover, the idea of the idea of the dirac sea not work for bosons at all even at this superficial level. It is secondorder in space and time and manifestly lorentzcovariant.
The square of dirac equation, calculated before can now be written in a simple, covariant form. What is the relationship between the dirac equation and the. Comparison among klein gordon equation, dirac equation and relativistic stationary schr. We show that these coordinates can be associated with a system with constant acceleration. Dirac wanted to fix the problems with the kleingordon equation by seeking a new solution to it. Components of dirac equation solve the klein gordan. The key result is the dirac equation, from which these predictions emerge. Physics 221b spring 2020 notes 45 introduction to the. With our service, you can drag and drop your pdf files and combine them into one in one click. Lecture 15 page 2 of 6 klein gordon equation 1926 schrodinger. The non relativistic limit of the real kleingordon equation. The development of quantum mechanics is presented from a historical perspective.
Electromagnetic kleingordon and dirac equations in scale relativity article pdf available in international journal of modern physics a 2522 september 2010 with 832 reads how we measure reads. The dirac equation is more restrictive than the kleingordon equation. Solutions of timedependent kleingordon and dirac equations. The separation of variables for the kleingordon and dirac equations, in the presence of electromagnetic fields, for a class of curvilinear coordinate systems with a null coordinate is presented. Initially, it was assumed that the 4dimensional space introduced by dirac could be. The dirac equation a great deal more was hidden in the dirac equation than the author had expected when he wrote it down in 1928. Pdf bound states of the kleingordon and dirac equations.