On properties of the discrete and continuous spectrum for the radial dirac equation

1996 ◽  
Vol 108 (1) ◽  
pp. 876-888 ◽  
Author(s):  
L. A. Sakhnovich
Keyword(s):  
Dirac Equation ◽  
Continuous Spectrum ◽  
Discrete And Continuous Spectrum ◽  
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.

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

Discrete and continuous spectrum in subwavelength imaging with wire-medium type lenses

2016 ◽  
Author(s):  
Francisco Mesa ◽  
Raul Rodriguez-Berral ◽  
George W. Hanson ◽  
Ali Forouzmand ◽  
Alexander B. Yakovlev ◽  
...  
Keyword(s):  
Continuous Spectrum ◽  
Subwavelength Imaging ◽  
Medium Type ◽  
Discrete And Continuous Spectrum

scholarly journals The Discrete and Continuous Retardation and Relaxation Spectrum Method for Viscoelastic Characterization of Warm Mix Crumb Rubber-Modified Asphalt Mixtures

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3723 ◽  
Author(s):  
Fei Zhang ◽  
Lan Wang ◽  
Chao Li ◽  
Yongming Xing
Keyword(s):  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Crumb Rubber ◽  
Asphalt Mixtures ◽  
Time Range ◽  
Modified Asphalt ◽  
Dynamic Modulus Test ◽  
Discrete And Continuous Spectrum

To study the linear viscoelastic (LVE) of crumb rubber-modified asphalt mixtures before and after the warm mix additive was added methods of obtaining the discrete and continuous spectrum are presented. Besides, the relaxation modulus and creep compliance are constructed from the discrete and continuous spectrum, respectively. The discrete spectrum of asphalt mixtures can be obtained from dynamic modulus test results according to the generalized Maxwell model (GMM) and the generalized Kelvin model (GKM). Similarly, the continuous spectrum of asphalt mixtures can be obtained from the dynamic modulus test data via the inverse integral transformation. In this paper, the test procedure for all specimens was ensured to be completed in the LVE range. The results show that the discrete spectrum and the continuous spectrum have similar shapes, but the magnitude and position of the spectrum peaks is different. The continuous spectrum can be considered as the limiting case of the discrete spectrum. The relaxation modulus and creep compliance constructed by the discrete and continuous spectrum are almost indistinguishable in the reduced time range of 10−5 s–103 s. However, there are more significant errors outside the time range, and the maximum error is up to 55%.

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