A possible approach to the two-body relativistic problem

1980 ◽  
Vol 56 (3) ◽  
pp. 263-288 ◽  
Author(s):  
D. Dominici ◽  
J. Gomis ◽  
G. Longhi
Keyword(s):  
Relativistic Problem

Continuous states for a relativistic problem plus tensor coupling in D-dimensional space

2015 ◽  
Vol 67 (7) ◽  
pp. 1118-1126 ◽  
Author(s):  
Mahdi Eshghi ◽  
Hosein Mehraban
Keyword(s):  
Dimensional Space ◽  
Tensor Coupling ◽  
Continuous States ◽  
Relativistic Problem

The relativistic problem of the right-angled lever: The correctness of the Laue solution

1969 ◽  
Vol 61 (2) ◽  
pp. 201-209 ◽  
Author(s):  
R. G. Newburgh
Keyword(s):  
Relativistic Problem ◽  
The Right

Bonding in Radon Hexafluoride: An Unusual Relativistic Problem?

ChemInform ◽  
2003 ◽  
Vol 34 (22) ◽  
Author(s):  
Michael Filatov ◽  
Dieter Cremer
Keyword(s):  
Relativistic Problem

scholarly journals EFFECTS OF A MIXED VECTOR-SCALAR KINK-LIKE POTENTIAL FOR SPINLESS PARTICLES IN TWO-DIMENSIONAL SPACE–TIME

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2609-2618 ◽  
Author(s):  
ANTONIO S. DE CASTRO
Keyword(s):  
Morse Potential ◽  
Dimensional Space ◽  
Liouville Problem ◽  
Bounded Solutions ◽  
Compton Wavelength ◽  
Apparent Paradox ◽  
Exactly Solvable ◽  
Relativistic Problem ◽  
Dimensional Space Time ◽  
Sturm Liouville

The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials (~ tanh γx) is investigated. The problem is mapped into the exactly solvable Sturm–Liouville problem with the Rosen–Morse potential and exact bounded solutions for particles and antiparticles are found. The behavior of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.

Relativistic problem of random flights and Nelson's stochastic mechanics

1992 ◽  
Vol 164 (1) ◽  
pp. 6-16 ◽  
Author(s):  
Piotr Garbaczewski
Keyword(s):  
Stochastic Mechanics ◽  
Random Flights ◽  
Relativistic Problem

Relativistische Verallgemeinerung des Lenzschen Vektors (I) / Relativistic generalisation of the Lenz vector (I)

1984 ◽  
Vol 39 (8) ◽  
pp. 720-732
Author(s):  
Eberhard Kern
Keyword(s):  
Angular Momentum ◽  
Kepler Problem ◽  
Coulomb Field ◽  
Equation Of Motion ◽  
Central Field ◽  
Relativistic Energy ◽  
Geometric Meaning ◽  
Type Curves ◽  
Relativistic Problem ◽  
Charged Nucleus

The non-relativistic motion of a particle in a central field with 1/r potential, e.g. the motion of an electron in the Coulomb field of a charged nucleus at rest, is described by the equation of motion (non-relativistic Kepler problem) m x″ = α · x /r3 with α = ez e (product of the charges of the central body ez and the electron e). From this equation of motion, three statements of conservation can be derived: in respect of the energy E, of the angular momentum L and of the Lenz vector Λ = m {x′× L + α ·x/r}. The geometric meaning of Λ is that of a vector pointing in the direction of the perihelion of the particle orbits (conic sections). It will be demonstrated that also at the relativistic Kepler problem, which is based on the equation of motion an analogous Lenz vector exists. It represents a quantity of conservation - in the same way as the relativistic energy and the relativistic angular momentum. For the transitional case → ∞, where the relativistic problem turns into the non-relativistic problem, the relativistic Lenz vector also turns into the non-relativistic Lenz vector. The generalised (relativistic) Lenz vector has also a geometric meaning. Its direction coincides with the oriented axis of symmetry of the orbits (rosettes, spirals, hyperbola-type curves etc.). The quantity of conservation Λ occupies a special position in respect of the quantities of conservation energy and angular momentum. Whereas the energy and the angular momentum correspond with a symmetry of time and space, the Lenz quantity of conservation corresponds with a symmetry of the orbits. The fact that the Lenz vector can relativistically be generalised touches thereby on principal aspects.

A Note on the Relativistic Problem of Uniform Rotation

1946 ◽  
Vol 69 (9-10) ◽  
pp. 488-491 ◽  
Author(s):  
E. L. Hill
Keyword(s):  
Uniform Rotation ◽  
Relativistic Problem

Complex eigenvalues in scattering theory

1959 ◽  
Vol 253 (1272) ◽  
pp. 16-36 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Excited States ◽  
Scattering Theory ◽  
Asymptotic Form ◽  
Outgoing Wave ◽  
Complex Energy ◽  
Channel One ◽  
Complex Eigenvalues ◽  
Relativistic Problem

The non-relativistic problem of scattering of a particle by a target possessing discrete excited states can be expressed in terms of ‘physical’ resonance states, i.e. solutions of the wave equation for complex energy in which in the asymptotic form of the wave function in each channel one of the two possible exponential terms (which for real energy represent the incoming and outgoing wave) vanishes. This representation is possible provided the interaction between the particles and the target vanishes exactly beyond a certain distance. If the interaction decreases exponentially a similar representation may in some cases still be obtained by analytic continuation; it contains also ‘redundant’ eigenstates in which the coefficient of one of the asymptotic waves tends to infinity. Possible generalizations of the method are discussed.

A relativistic problem: The charge distribution stability on a conductor

1981 ◽  
Vol 49 (5) ◽  
pp. 501-503 ◽  
Author(s):  
A. Hernández ◽  
M. Rivas
Keyword(s):  
Charge Distribution ◽  
Relativistic Problem

Inverse relativistic problem for the bound quark-antiquark states

1982 ◽  
Vol 45 (2) ◽  
pp. 291-299 ◽  
Author(s):  
L. Aleksandrov ◽  
M. Drenska ◽  
D. Karadjov ◽  
P. Morozov
Keyword(s):  
Relativistic Problem
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