However, interpretation of solutions of these equations as probability densities are problematic in case of the klein gordon equation, the predicted. We explore klein gordon equation in the new framework of quasihermitian quantum mechanics. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist paul dirac in 1928. Out of this analysis will emerge the kleingordon and dirac equations, and the concept of quantum mechanical spin. It describes advanced properties of nature on an atomic scale classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature.
The dirac equation can be derived by factoring the klein gordon equation not the solutions. What is the relationship between the dirac equation and. Solutions to common problems with probability interpretation and inde. You mean using a relativistic field equation to predict the bound states etc. P a m dirac, the principles of quantum mechanics, 4th ed. To construct a relativistic wave equation we shall use the relations that provide the transition from classical mechanics to quantum mechanics. Wave equations concentrates mainly on the wave equations for spin0 and spin12 particles. In relativistic quantum mechanics schroedingers equation is replaced by the klein gordon and. Relativistic quantum mechanics online course video. The dirac equation relativistic spectrum is, however, easily recovered if the. It gives a thorough analysis of the klein gordon and dirac equations highlighting their properties.
Relativistic quantum mechanics 128 further symmetries will be taken up in the chapter on symmetries and transformation groups. Apoorva d patel,department of physics,iisc bangalore. The chapters that follow introduce the dirac equation, investigate its covariance. Its solutions include a quantum scalar or pseudoscalar field, a field whose. Relativistic quantum mechanics download ebook pdf, epub. Relativistic quantum mechanics video course course outline dirac and klein gordon equations, lorentz and poincare groups, fundamental processes of quantum electrodynamics. How did paul dirac unify quantum mechanics and special.
Hence, people tried to come up with a lorentzinvariant evolution equation for the wave function such as the klein gordan and dirac equations as mentioned by anna v. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was. Notes on relativistic quantum mechanics module 4 of. Newest kleingordonequation questions physics stack. It was shown that this leads to the klein gordon equation from which some fundamental physics follows. Klein gordon equation for simplicity, we begin from a particle with mass m 0 but without spin. Why the schrodinger equation fails at relativity youtube. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one and threedimensional box using the klein gordon. I go over fourvector notation, fourgradient, and writing the equation. It provides valuable insights into the underlying physics.
This book aims at addressing this gap by providing a lucid description of single particle relativistic dynamics at the quantum scale adapting, in a sense, the schrodinger wave equations. For full reconciliation of quantum mechanics with special relativity, quantum. Chapter 1 deals with the klein gordon equation and its properties and applications. Relativistic wave equation klein fock gordon equation. Relativistic quantum mechanics 1 need for relativistic quantum mechanics.
P m mathews and k venkatesan, a textbook of quantum mechanics, tata mcgrawhill 1977 chapt 10. Does this also apply for solutions of klein gordon equation or dirac equation or other relativistic wave equations. It turns out that the form of the relativistic equation depends on the spin of the particle, spin0 klein gordon equation spin12 dirac equation. Although the earlier formulations, like the schrodinger picture and heisenberg picture were originally formulated in a non relativistic background, a few of them e. The fast oscillating exponential is the solution for the particle at rest. Note that we have derived this equation from something that did give the right answers so we expect the dirac equation. It is secondorder in space and time and manifestly lorentzcovariant. The attempts to generalize it to the relativistic case led to the discovery of various wave equations klein gordon, dirac, maxwell. Hamitonian, we act h again on the dirac wave function and find. The chapters that follow introduce the dirac equation, investigate its covariance properties and present various approaches to obtaining solutions.
Relativistic quantum mechanics wave equations concentrates mainly on the wave equations for spin0 and spin12 particles. Kleingordon equation relativistic quantum mechanics. The role of the kleingordon equation in relativistic. The first chapter deals with the klein gordon equation and. It is a quantized version of the relativistic energymomentum relation. Lorentzinvariant di erential equations which take the place of the schr odinger equation of a particle of mass mand charge qin an electromagnetic eld c. Electromagnetic interactions are also stud ied in the context of the minimal coupling prescription. Introduction to relativistic quantum mechanics 249 1. Mod01 lec01 introduction, the kleingordon equation.
A brief introduction to relativistic quantum mechanics. Oneparticle states and their lorentz transforma tions follow, leading to the klein gordon and the dirac equations for probability amplitudes. In classical quantum mechanics, absolute square of the wave function i. At the very least it should be consistent with the theory of spe cial relativity that had revolutionized classical physics. Its theoretical relevance is similar to that of the dirac equation. Out of this analysis will emerge the klein gordon and dirac equations, and the concept of quantum mechanical spin. The klein gordon equation klein fock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. How to use the einstein energymomentum relation to derive the klein gordon wave equation. Relativistic quantum mechanics begins with the klein gordon equation describing its features and motivating the need for a correct relativistic equation for the electron. Youd have to use qed, the klein gordon and free dirac fields dont account for electromagnetic interactions, well the latter can if you apply minimal coupling but without quantum field theory one can only account for first order interactions. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist.
Published on sep 25, 2019 i derive the klein gordon equation. The final formalism of dealing with the relativistic quantum equations has been developed since that time and is now called the quantum field theory. Starting with the relativistic indentity, that rest mass is the magnitude of the energy momentum 4vector, and replacing momentum with the differential operator which represents momentum in quantum mechanics we have the klein gordon equation dirac. During the early part of the last century schrodingers equation was used to explain and describe all phenomena in atomic. This introduction prepares the way for the construction of relativistic quantum. Klein gordon equation the quest for a mathematical theory of quantum mechanics began with great am bition. Introduction, the klein gordon equation particles and antiparticles, two component framework coupling to electromagnetism, solution of the coulomb problem bohrsommerfeld semiclassical solution of the coulomb problem, the dirac equation and the clifford algebra dirac matrices, covariant form of the dirac equation, equations of motion, spin. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. It then introduces the dirac equation by linearizing the second order relativistic equation which reveals the spin, spin magnetic moment and the spinorbit. Comparison among kleingordon equation, dirac equation. R shankar, principles of quantum mechanics, 2nd ed.
It is consistent with both the principles of quantum mechanics and the theory of special relativity. 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. He then tried to find solutions, but was dismayed to find that problems like nonpositivedefinite probability curre. Deriving the klein gordon equation relativistic quantum. To what extent is standard quantum mechanics actually non.
Then its kinetic energy reads 1 2 m 0v 2 with velocity vbeing unlimited and m 0 unchanged. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and. It is immediate that if the mass m vanishes, as in the case of a photon, kge reduces to the standard electromagnetic. 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. Lecture 22 relativistic quantum mechanics theory of condensed. Now we would like to extend quantum mechanics to the relativistic domain. Course detail module 1 klein gordon and dirac equations lecture 1 introduction, the klein gordon equation lecture 2 particles and antiparticles, two component framework. On a deeper level, these two requirements can actually be considered one and the same. R parthasarathy, relativistic quantum mechanics, narosa 2009. The klein gordon equation and relativistic quantum. Relativistic quantum mechanics janos polonyi university of strasbourg dated. Deriving the klein gordon equation relativistic quantum youtube.
The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. When we appropriately square the dirac equation, the. Relativistic quantum mechanics rqm is quantum mechanics applied with special relativity. Why the schrodinger equation fails at relativity andrew dotson. The kleingordon equation or the klein fock gordon equation is an equation in quantum field theory which initially was discovered by schrodinger but discarded by him soon after. Deriving the klein gordon equation relativistic quantum duration. In non relativistic quantum mechanics, if the hamiltonian commutes with j, the angular momentum operator that is a generator of the su2 group, it will be rotationally invariant and after a rotation the system will still obey schroedingers equation. Im starting to wonder if spin is a relativistic thing, but i know that i studied it in griffiths introduction to quantum mechanics, which is all non relativistic. Relativistic quantum mechanics kleingordon equation dirac. Readers who want to get to rqm quickly, without studying its foun.
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