A modified dirac equation has been described by fredsted 17 as the square root of klein gordon equation with mass advantages. But there also exists a pair of equations for spin12 particles that consists of a kleingordonlike equation being a direct consequence of the dirac equation. Chapter 21 relativistic quantum fields the quantized maxwell. Em lorentz force derived from klein gordon s equation 11.
Diracs solution to the kleingordon equation physics forums. Dirac and kleingordon equations with equal scalar and. But we have four dirac operators and only three pauli operators. For a free particle, each component of the dirac spinor satisfies the klein gordon equation. The elementary solutions have a position dependence of the form eik. Deriving the klein gordon equation relativistic quantum. Separation of variables and exact solution of the klein.
Continuity equation 99,103 for neutrino currents 337 for the klein gordon field 42 of the klein gordon equation 6 continuum waves 248 of negative energy 199 contravariant 2 coordinate inversion 397 correlation diagram 274 relativistic 274 coulom barrier 261 coulomb energy, expectation value of the 226 coulomb gauge 51. Dirac wanted to fix the problems with the klein gordon equation by seeking a new solution to it. Klein gordon equations in one space dimension, employing a null form estimate and a. Vagenas 3 1 physics department and cfisuc, univer sity of coimbra, p3004. The maxwell dirac system describes the interaction of an electron with its own electromagnetic field. Generalized dirac and kleingordon equations for spinor. Comparison among klein gordon equation, dirac equation and relativistic stationary schr. But why did it need to be of first order in time and. Quantum field theory i babis anastasiou institute for theoretical physics, eth zurich, 8093 zurich, switzerland. Dirac equation from the kleingordon one as for the free particle motion, i. On the other hand, the klein paradox, as of this writing, is a hot topic in the area of graphene physics. Pdf we present a new step in the foundation of quantum field theory with. The new generalized dirac and klein gorodon equations are obtained by using nonzero phase factors, and these equations reduce to the standard dirac and klein gordon equations once the phase function is set to zero. Relativistic quantum mechanics kleingordon equation dirac.
Therefore, a system that can be described by a complex solution to the klein gordon equation also be described by a system of two independent particles with equal mass that have real solutions to the klein klein gordon equation. Dirac fine structure increased 3p32, 3d32 2sl2 12 lamb shift increased hyperfine structure increased bohr levels. A similar situation prevails for the klein gordon equation. 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. 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. In sections 3 and 4, we deal with the construction of potentials for the kleingordon and dirac equations respectively. Dirac equation in 1928 dirac tried to understand negative energy solutions by taking the squareroot of the klein gordon equation.
In order to be algebraic equivalent to dirac equation, their equations are forced to break the automorphism group of quaternions. We compare the solutions and the energy spectra obtained with the corresponding ones from the dirac equation for a spin onehalf relativistic particle. The spinor of mass minimally coupled to gravity is described by the dirac equation with. I go over fourvector notation, fourgradient, and writing the equation. A generalized klein gordon equation with a closed system.
Pdf electromagnetic kleingordon and dirac equations in scale. Iii we separate variables and solve the klein gordon equation. In sec iv, using the algebraic method of separation of variables, we reduce the dirac equation to a system of rst order coupled di erential equations that we solve in terms of special functions. Pdf stationary solutions of the maxwelldirac and the. It is secondorder in space and time and manifestly lorentzcovariant. Dirac current, the dirac adjoint and the use of the dirac equation to prove the continuity equation for the dirac current, its generalization into a dirac probability or. Pdf a discrete scheme for the dirac and kleingordon. Schroeder, addisonwesley 3quantum field theory in a nutshell, a. We study the thermodynamic quantities such as the helmholtz free energy, the mean energy and the specific heat for both the klein gordon, and dirac equations. Pdf dirac and kleingordon equations in curved space. The klein gordon equation klein fock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. What exactly goes wrong when using the kleingordon. The discovery of dirac equation and its impact on present.
The dirac equation we will try to find a relativistic quantum mechanical description of the electron. Before the advent of quantum theory, newtonian mechanics dictated a direct approach to particles and motion. It is a quantized version of the relativistic energymomentum relation. The timedependent klein gordon and dirac equations are solved for the motion of a charged particle in a classical uniform electrostatic field of infinite extent. In other words, the klein gordon equation, if useful at all, does not describe the probability wave, which the schrodinger equation does, but describes something else.
The fifth term is the so called darwin term which we said would come from the dirac equation. Its theoretical relevance is similar to that of the dirac equation. Comparison among kleingordon equation, dirac equation. Chapter 11 em lorentz force derived from klein gordons. Comparison of squared dirac fokivanenko equation for a spin particle with klein gordon equation in curved space has given an expression for chiral spin current variation through the derivative of. The obvious way of creating a manifestly invariant wave equation is to start from the well known relativistic energy equation and. Solutions to common problems with probability interpretation and inde. Historically, dirac 1928 was looking for a covariant wave equation that was firstorder in time. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation.
A general solution of kgd equation as a superposition of two dirac plane harmonic waves with different masses has been obtained. Accordingly, the kleingordon kg equation and dirac equation are restudied and compared with the relativistic stationary schrodinger equation rsse. In the dirac case, the discrete solution converges to the continuum propagator and it can also be rewritten in the form. Dirac equation, kleingordon equation, scalar and vector coupling, noncentral potentials, relativistic extensions, hartmann potential, morse potential. He wanted a relativistic solution so it makes sense that the solution needed to satisfy einsteins energymomentum relation. Klein gordon equation f eynman stuec k elburg in terpretation dirac equation an tiparticles f ermion spin co v arian t notation massless fermions learning outcomes be able to deriv e k g equation and explain ph ysical meaning of v e e solutions. Comparison among kleingordon equation, dirac equation and. In the present work, we like to study the cauchy problem for the dirac klein gordon equations.
By introducing the concept of system mass into the klein. In many textbooks and lecture notes, it says that the klein gordon equation was discarded first because when interpreting it as an equation for a singleparticle wave function and trying to calcula. Resonance j august 2003 g rajasekaran the major events in the discovery of the dirac equation and its interpretation are traced. A large number of potentials have been constructed. In contrast to the klein gordon case, the situation is more complicated in the case of the dirac equation and this complication is basically due to the square root, which appears in the expressions of and. Kleingordon and dirac equations with thermodynamic. Both the klein gordon and the dirac equation are no 1particle wave equations, but relativistic. Hamitonian, we act h again on the dirac wave function and find. The dirac equation is one of the two factors, and is conventionally taken to be p m 0 31 making the standard substitution, p.
For comparison, we have also discussed the dirac equation. How to use the einstein energymomentum relation to derive the klein gordon wave equation. The transmission coefficient is derived by the matching conditions on the wavefunctions and the condition for the existence of transmission resonances are investigated. We explore klein gordon equation in the new framework of quasihermitian quantum mechanics. Stationary solutions of the kleingordon equation in a. The schrodinger equation relativistic quantum mechanics the klein gordon equation, the dirac equation, angular momentum and spin, symmetries of the dirac equation quantum electrodynamics classical electromagnetism, the dirac equation in an electromagnetic field scattering and. Because of this reason, the klein gordon equation was abandoned for a while. We will come back to the question what it actually describes later on.
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