Verfahren zur näherungsweisen Anpassung einer Lösung der Schrödinger‐ an die Diracgleichung

Sommerfeld, Arnold; Maue, A. W.

doi:10.1002/andp.19354140703

Cited by 112 publications

(35 citation statements)

References 12 publications

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“…In this approximation, the wave functions and the Green's functions of the Dirac equation in the external field have very simple forms which drastically simplify their use in specific calculations. The wave functions, obtained in the leading quasiclassical approximation for the Coulomb field, are the famous Furry-Sommerfeld-Maue wave functions [8,9] (see also Ref. [5]).…”

Section: Introductionmentioning

confidence: 99%

Charge asymmetry in the differential cross section of high-energy bremsstrahlung in the field of a heavy atom

Krachkov

Milstein

2015

Phys. Rev. A

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The distinction between the charged particle and antiparticle differential cross sections of highenergy bremsstrahlung in the electric field of a heavy atom is investigated. The consideration is based on the quasiclassical approximation to the wave functions in the external field. The charge asymmetry (the ratio of the antisymmetric and symmetric parts of the differential cross section) arises due to the account for the first quasiclassical correction to the differential cross section. All evaluations are performed with the exact account of the atomic field. We consider in detail the charge asymmetry for electrons and muons. For electrons, the nuclear size effect is not important while for muons this effect should be taken into account. For the longitudinal polarization of the initial charged particle, the account for the first quasiclassical correction to the differential cross section leads to the asymmetry in the cross section with respect to the replacement ϕ → −ϕ, where ϕ is the azimuth angle between the photon momentum and the momentum of the final charged particle.

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Section: Introductionmentioning

confidence: 99%

Charge asymmetry in the differential cross section of high-energy bremsstrahlung in the field of a heavy atom

Krachkov

Milstein

2015

Phys. Rev. A

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Quantum electrodynamics processes in the interaction of high-energy particles with atoms

Krachkov¹,

Li²,

Mil'shtein³

2016

Успехи физических наук

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“…Apart from the bound states (19), approximate continuum wavefunctions can be derived which are accurate to αZ in the relativistic motion of the electron and which are known as Sommerfeld-Maue wavefunctions [22] from the literature. Again, these functions can be expressed in terms of the nonrelativistic functions and have been widely used in applications [21,23].…”

Section: Semirelativistic Frameworkmentioning

confidence: 99%

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

Surzhykov

Koval

Fritzsche

2005

Computer Physics Communications

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Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the Dirac program which has been developed originally for studying the properties and dynamical behaviour of the (hydrogen-like) ions. In the present version, a set of Maple procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the Dirac program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. * To whom correspondence should be addressed (surz@physik.uni-kassel. Keywords: Analytical solution, Coulomb-Green's function, Coulomb problem, Dirac equation, energy level, expectation value, hydrogen-like ion, hydrogenic wavefunction, matrix element, radial integral, special functions. Nature of the physical problem:Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure of the hydrogen-like ions, however, the underlying 'mathematics' is not always that easy to deal with. Apart from the well-known level structure of these ions as obtained from either the Schrödinger or Dirac equation, namely, a great deal of other properties are often needed. These properties are related to the interaction of bound electron(s) with external particles and fields and, hence, require to evaluate transition amplitudes, including wavefunctions and (transition) operators of quite different complexity. Although various special functions, such as the Laguerre polynomials, spherical harmonics, Whittaker functions, or the hypergeometric functions of various kinds can be used in most cases in order to express these amplitudes in a concise form, their derivation is time consuming and prone for making errors. In addition to their complexity, moreover, there exist a large number of mathematical relations among these functions which are difficult to remember in detail and which have often hampered quantitative studies in the past. Method of solution:A set of Maple procedures is developed which provides both the nonrelativistic and relativistic (analytical) solutions of the 'hydrogen atom model' and which facilitates the symbolic evaluation of various transition amplitudes. 2 Restrictions onto the complexity of the problem:Over the past decades, a large number of representati...

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Verfahren zur näherungsweisen Anpassung einer Lösung der Schrödinger‐ an die Diracgleichung

Cited by 112 publications

References 12 publications

Charge asymmetry in the differential cross section of high-energy bremsstrahlung in the field of a heavy atom

Charge asymmetry in the differential cross section of high-energy bremsstrahlung in the field of a heavy atom

Quantum electrodynamics processes in the interaction of high-energy particles with atoms

Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

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