On the phase-integral method for the radial Dirac equation

2009 ◽  
Vol 42 (39) ◽  
pp. 395203 ◽  
Author(s):  
Giampiero Esposito ◽  
Pietro Santorelli
Keyword(s):  
Dirac Equation ◽  
Integral Method ◽  
Phase Integral ◽  
Radial Dirac Equation

The Jost function treated by the F-matrix phase integral method

1979 ◽  
Vol 12 (2) ◽  
pp. 171-186 ◽  
Author(s):  
G Drukarev ◽  
N Froman ◽  
P O Froman
Keyword(s):  
Integral Method ◽  
Matrix Phase ◽  
Jost Function ◽  
Phase Integral

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.

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