Approximate solutions of Dirac equation for Tietz and general Manning-Rosen potentials using SUSYQM

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

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Approximate solutions of Dirac equation with a ring-shaped Woods-Saxon potential by Nikiforov-Uvarov method

Chinese Physics C ◽

10.1088/1674-1137/37/11/113104 ◽

2013 ◽

Vol 37 (11) ◽

pp. 113104 ◽

Cited By ~ 2

Author(s):

H. Hassanabadi ◽

E. Maghsoodi ◽

S. Zarrinkamar

Keyword(s):

Dirac Equation ◽

Approximate Solutions ◽

Saxon Potential ◽

Uvarov Method

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BLACK HOLE PHYSICS, CONFINING SOLUTIONS OF SU(3)-YANG– MILLS EQUATIONS AND RELATIVISTIC MODELS OF MESONS

Modern Physics Letters A ◽

10.1142/s0217732301003784 ◽

2001 ◽

Vol 16 (09) ◽

pp. 557-569 ◽

Cited By ~ 17

Author(s):

YU. P. GONCHAROV

Keyword(s):

Black Hole ◽

Dirac Equation ◽

Exact Solutions ◽

Bound States ◽

Black Hole Physics ◽

Approximate Solutions ◽

Yang Mills ◽

Minkowski Space Time ◽

Relativistic Models ◽

Relativistic Bound States

The black hole physics techniques and results are applied to find a set of exact solutions of the SU(3)-Yang–Mills equations in Minkowski space–time in the Lorentz gauge. All the solutions contain only the Coulomb-like or linear in r components of SU(3)-connection. This allows one to obtain some possible exact and approximate solutions of the corresponding Dirac equation that can describe the relativistic bound states. Possible application to the relativistic models of mesons is also outlined.

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SPINOR PARTICLES IN THE SPACETIMES OF VACUUMLESS DEFECTS

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512008161 ◽

2012 ◽

Vol 18 ◽

pp. 31-37

Author(s):

SANDRO G. FERNANDES ◽

GEUSA DE A. MARQUES ◽

V. B. BEZERRA

Keyword(s):

Dirac Equation ◽

Approximate Solutions ◽

Gravitational Fields

We obtain approximate solutions of the Dirac equation in the gravitational fields of vacuumless defects. In all obtained solutions we show the role played by the presence of these defects.

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Approximate Solutions of the Dirac Equation for the Manning-Rosen Potential Including the Spin-Orbit Coupling Term

International Journal of Theoretical Physics ◽

10.1007/s10773-008-9887-7 ◽

2008 ◽

Vol 48 (4) ◽

pp. 1142-1149 ◽

Cited By ~ 28

Author(s):

F. Taşkın

Keyword(s):

Dirac Equation ◽

Approximate Solutions ◽

Orbit Coupling ◽

Spin Orbit Coupling ◽

Spin Orbit ◽

Coupling Term ◽

Rosen Potential

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Effect of Quantum Inhomogeneity Corrections in Semi-Statistical Thomas–Fermi Calculations for Atoms

Canadian Journal of Physics ◽

10.1139/p74-253 ◽

1974 ◽

Vol 52 (19) ◽

pp. 1926-1932 ◽

Cited By ~ 2

Author(s):

J. A. Stauffer ◽

J. W. Darewych

Keyword(s):

Dirac Equation ◽

Variational Method ◽

Quantum Correction ◽

Correction Term ◽

Approximate Solutions ◽

The Other ◽

Gradient Term ◽

Gradient Expansion ◽

Thomas Fermi ◽

Correction Terms

Approximate solutions to the Thomas–Fermi equation with so-called 'quantum correction terms' have been obtained by the use of a variational method. The results for krypton support the conclusions of Tomishima and Yonei that the coefficient of the gradient term should be 9/5 of the value derived by Kirzhnits. On the other hand, when the use of these equations is restricted to a region of the atom where the gradient expansion of Kirzhnits might be expected to be valid, the Kirzhnits value of the constant gives the better results, but the best results are obtained with no correction term at all (i.e. with the Thomas–Fermi–Dirac equation).

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