Non relativistic limit of klein gordon equation pdf

The non relativistic viewpoint implicit in the form of the coupling in eq. The non relativistic limit of the dirac equation one important requirement for the dirac equation is that it reproduces what we know from non relativistic quantum mechanics. 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. However, the kleingordon equation does not lead to a positive. We consider numerics asymptotics for the rotating nonlinear kleingordon rkg equation, an important pde in relativistic quantum physics that can model a rotating galaxy in. Pdf nonrelativistic limit of kleingordonmaxwell to. About the nonrelativistic limit of the phase velocity of.

Oct 28, 2009 hi, i have a conceptual question about taking non relativistic nr limits of the klein gordon equation, inspired by zees book on qft chapter iii. The kleingordon equation is lorentz invariant for two reasons. In the nonrelativistic limit, the formalism reduces naturally to that of the schr\odinger equation. I just have a question regarding assessing the nonrelativistic limit of the kleingordon equation. Nonrelativistic limit of scattering theory for nonlinear.

There is a close algebraic analogy between 1 the helmholtz equation governing scalar optics and the kleingordon equation and 2 the matrix form of maxwells equations governing. What is the role of the factor eimt used in the derivation of s equation from. Nonrelativistic limit of klein gordon and massless. Nonrelativistic limit of kleingordonmaxwell to schrodingerpoisson. The problem of the equivalence between the relativistic schrodinger equation and the kleingordon equation is also addressed by using arguments which can be understood by undergraduate students. It is secondorder in space and time and manifestly lorentzcovariant. Overall, the kleingordon equation appears to be a good relativistic replacement for the nonrelativistic schr. Journal of mathematical analysis and applications 71, 3647 1979 on the nonrelativistic limits of the kleingordon and dirac equations andrew y.

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. The paper also shows that in classical limit the hydrodynamic klein gordon equations lead to the madelung pseudopotential 1 as well as to the quantum pseudo potential for a charged particle given by janossy 2. Limits used to find nonrel limit of the kleingordon equation. Exact bound states of the ddimensional klein gordon equation 1427 the radial and angular parts of the klein gordon equation with this type of potential are solved using the nu method. On timesplitting pseudospectral discretization for. Note that we have derived this equation from something that did give the right answers so we expect the dirac equation to pass this test. Relativistic quantum mechanics kleingordon equation dirac. Fourmomentum a free particle in the non relativistic limit obeys. Kleingordon equation nonrelativistic limit link to. Comparison among kleingordon equation, dirac equation and relativistic stationary schr.

Journal of mathematical analysis and applications 71, 3647 1979 on the nonrelativistic limits of the klein gordon and dirac equations andrew y. Nonexistence of a probability for the klein gordon equation. For a long time, it was believed that the dirac equation was. Lecture 22 relativistic quantum mechanics theory of condensed. We use and motivate a splitting of the scalar kleingordon field into a sum of two fields, corresponding, in the physical. Heuristic derivation of the klein gordon equation 11 b. Pdf the schrodingernewton equation as nonrelativistic. For the complete study of the nonrelativistic limit of the cauchy problem for the nonlinear kleingordon equation we will refer to machiharanakanishiozawa 20 see also 24, 26 and references. We now want to reconcile the principles of quantum mechanics with special relativity. It is a quantized version of the relativistic energymomentum relation. On timesplitting pseudospectral discretization for nonlinear. On timesplitting pseudospectral discretization for nonlinear kleingordon equation in nonrelativistic limit regime volume 16 issue 2 xuanchun dong, zhiguo xu, xiaofei zhao. Nonrelativistic limit of the klein gordon equation.

The non relativistic limit of the kleingordon equation kg is the schrodinger equation s. The non relativistic limit of the klein gordon equation kg is the schrodinger equation s. To describe the particle at particle colliders we need to incorporate special theory of relativity 8 2. In the non relativistic limit, the formalism reduces naturally to that of the schr\odinger equation. Notes on relativistic quantum mechanics module 4 of. That is where cryptohermitian approach can be applied. Nonrelativistic limit of klein gordon and massless limits. The paper also shows that in classical limit the hydrodynamic kleingordon equations lead to the madelung pseudopotential 1 as well as to the quantum pseudo potential for a. Asymptotic approximating schemes for the kleingordon. The non relativistic limit of the kleingordon equation kg is the. Chapter 7 relativistic quantum mechanics in the previous chapters we have investigated the schr. This is a case where an incautious assumption at the outset led to misinterpretation.

Nonrelativistic limit in the energy space for nonlinear. The schrodinger newton equation as nonrelativistic. Cant the negative probabilities of klein gordon equation be avoided. Stationary solutions of the kleingordon equation in a. In this paper we give a mathematical proof that the kleingordon and dirac equations of relativistic quantum mechanics have the correct nonrelativistic limits.

In its free form, or including electromagnetic interactions, it describes all spin1 2 massive particles such as electrons and quarks for which parity is a symmetry. We study the nonrelativistic limit of the cauchy problem for the nonlinear kleingordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear schrodinger equation in the energy space, after the infinite oscillation in time is removed. Nonrelativistic limit of the nonlinear kleingordon equation. Comparison among kleingordon equation, dirac equation. Pasquali 1universit a dellaquila 2universit a degli studi di milano 2016, march 22 d. Comparison among kleingordon equation, dirac equation and. The nonrelativistic limit of the dirac equation one important requirement for the dirac equation is that it reproduces what we know from nonrelativistic quantum mechanics. Klein gordon equation the schrodinger equation only describes particles in the non relativistic limit. Note that we have derived this equation from something that did give the right answers so. On the nonrelativistic limits of the kleingordon and dirac equations. In page 42 of david tongs lectures on quantum field theory, he says that one can also derive the schrodinger lagrangian by taking the nonrelativistic limit of the complex. On timesplitting pseudospectral discretization for nonlinear klein gordon equation in nonrelativistic limit regime volume 16 issue 2 xuanchun dong, zhiguo xu, xiaofei zhao.

Pdf singular limits of the kleingordon equation researchgate. Relativistic quantum mechanics janos polonyi university of strasbourg dated. In particular, in 18 machiharanakanishiozawa proved that any nite energy solution converges to the corresponding solution of the nonlinear schr odinger equation in the energy space, after in nite oscillations in time are removed. Nonrelativistic limit of the nonlinear kleingordon. Deriving the klein gordon equation relativistic quantum. The relativistic quantum hydrodynamic representation of. Nonrelativistic limit in the energy space for nonlinear klein. The full consistency with quantum mechanics will eventually be recovered by.

I just have a question regarding assessing the non relativistic limit of the klein gordon equation. Pauli and weisskopf in 1934 showed that kleingordon equation describes a spin0 scalar eld. On the nonrelativistic limits of the kleingordon and. The conclusion that the kleingordon equation is a relativistic extension of the schrodinger. About the nonrelativistic limit of the phase velocity of matter waves. In the nonrelativistic limit in the static gravitational field, with the. Analysis and comparison of numerical methods for the klein. The schrodingernewton equation as nonrelativistic limit of selfgravitating klein gordon and dirac fields article pdf available in classical and quantum gravity 2921 june 2012 with 251 reads. The relativistic quantum hydrodynamic representation of klein. The klein gordon equation klein fock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation.

The dirac equation we will try to find a relativistic quantum mechanical description of the electron. However, the equation does not carry a probabilistic interpretation. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist paul dirac in 1928. Pauli equation in the nonrelativistic limit, spin can be introduced using the pauli equation which describes the interaction of a spin 12 particle with an external electromagnetic. Numerical methods for computing ground states and dynamics of nonlinear relativistic hartree equation for boson stars, j. Kleingordon equation derivation and continuity equations 3 energies, were taken to be major problems with the kleingordon equation which led to it being disregarded initially as a valid relativistic equation. Apparently, schrodinger tried out klein equation before proceeding with his nonrelativistic equations, but dropped it seeing many problems and never published it this equation was discarded in the community as faulty in addition, it did not leave any room for spi n.

Notes on relativistic quantum mechanics module 4 of refresher. In the limit m 0, the dirac equation reduces to the weyl equation, which describes relativistic massless spin 1. Introduction to relativistic quantum mechanics 250 an equation in relativistic quantum field theory. For the complete study of the non relativistic limit of the cauchy problem for the nonlinear klein gordon equation we will refer to machiharanakanishiozawa 20 see also 24, 26 and references. A complex field remains a complex field as expected for non relativistic problems where we are all familiar with wave functions and their interpretation. About the non relativistic limit of the phase velocity of matter waves.

For comparison, we have also discussed the dirac equation. On the nonrelativistic limits of the kleingordon and dirac. Both the dirac equation and the adjoint dirac equation can be obtained from varying the action with a specific lagrangian density that is given by. A complex field remains a complex field as expected for nonrelativistic problems where we are all familiar with wave functions and their interpretation. We develop the nonrelativistic limit of the dirac equation and action in the. Nonrelativistic limit of klein gordon maxwell to schrodingerpoisson. It is obtained in the nonrelativistic limit of the dirac equation by assuming the presence of an electromagnetic. It discusses properties of the equation and its continuity equation based on a comparison with the schrodinger equation and its continuity equation. Nonrelativistic limit of klein gordon equation kit. How to use the einstein energymomentum relation to derive the klein gordon wave equation.

For a long time, it was believed that the dirac equation was the only valid equation for massive particles. Pdf the schrodingernewton equation as nonrelativistic limit of. Pasquali 1universit a dellaquila 2universit a degli studi di milano. Lax introduction in this paper we give a mathematical proof that the kleingordon and dirac equations of relativistic quantum mechanics have. There are two such equations, one called the kleingordon and the other one called the dirac equation. Kleingordon equation the kleingordon equation can similarly be obtained from the rstquantization of a relativistic particle. One can show that in the non relativistic limit, the known expressions for the probability density and current are recovered. Kleingordon equation nonrelativistic limit pingback. Hi, i have a conceptual question about taking nonrelativistic nr limits of the kleingordon equation, inspired by zees book on qft chapter iii. Lax introduction in this paper we give a mathematical proof that the klein gordon and dirac equations of relativistic quantum mechanics have the correct. Schoene1 general motors research laboratories, warren, michigan 48090 submitted by peter d. The schrodinger equation is not relativistically invariant.