Phase-integral solution of the radial Dirac equation

2010 ◽  
Vol 51 (3) ◽  
pp. 032304 ◽  
Author(s):  
Staffan Linnæus
Keyword(s):  
Dirac Equation ◽  
Integral Solution ◽  
Phase Integral ◽  
Radial Dirac Equation

scholarly journals A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
ZiLong Zhao ◽  
ZhengWen Long ◽  
MengYao Zhang
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Bethe Ansatz ◽  
Dirac Oscillator ◽  
Solvable Models ◽  
Ansatz Method ◽  
Radial Dirac Equation

The generalized Dirac oscillator as one of the exact solvable models in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic, and sixth power potentials in radial Dirac equation were further given by means of the Bethe ansatz method. And finally, the corresponding exact solutions in this paper were further discussed.

scholarly journals Dirac Equation in the Field of a Charged Cosmic String and in the Field of a Point Charge with Z > 137

1991 ◽  
Vol 44 (6) ◽  
pp. 585
Author(s):  
TJ Allen ◽  
LJ Tassie
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Internal Structure ◽  
Effective Potential ◽  
Cosmic String ◽  
Point Charge ◽  
Schrodinger Equation ◽  
Cylindrical Coordinates ◽  
Line Charge ◽  
Radial Dirac Equation

In both spherical and cylindrical coordinates, the radial Dirac equation can be written in the form of a Schrodinger equation with an effective potential. It is shown that the difficulties at r -+ 0 for the Dirac equation in the field of a point charge for Z > 137 are the same as those for the Schrodinger equation with a l/r2 potential. The effective potential is used to show that similar difficulties do not arise for the field of a line charge, so allowing the consideration of the motion of electrons in the field of a charged superconducting cosmic string without considering the internal structure of the string.

scholarly journals DIRAC OSCILLATORS AND QUASI-EXACTLY SOLVABLE OPERATORS

2005 ◽  
Vol 20 (25) ◽  
pp. 1875-1885 ◽  
Author(s):  
Y. BRIHAYE ◽  
A. NININAHAZWE
Keyword(s):  
Dirac Equation ◽  
Dirac Operator ◽  
Spherically Symmetric ◽  
Dirac Oscillator ◽  
Generic Polynomial ◽  
Exactly Solvable ◽  
Spectral Equation ◽  
Radial Variable ◽  
Radial Dirac Equation

The Dirac equation is formulated in the background of three types of physically relevant potentials: scalar, vector and "Dirac-oscillator" potentials. Assuming these potentials to be spherically-symmetric and with generic polynomial forms in the radial variable, we construct the corresponding radial Dirac equation. Cases where this linear spectral equation is exactly solvable or quasi-exactly solvable are worked out in details. When available, relations between the radial Dirac operator and some super-algebra are pointed out.

The propagator of the radial Dirac equation

2002 ◽  
Vol 43 (8) ◽  
pp. 3963-3983 ◽  
Author(s):  
Takashi Ichinose ◽  
Brian Jefferies
Keyword(s):  
Dirac Equation ◽  
Radial Dirac Equation
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