Darboux transformations of the one-dimensional stationary Dirac equation

2002 ◽  
Vol 35 (14) ◽  
pp. 3279-3287 ◽  
Author(s):  
N Debergh ◽  
A A Pecheritsin ◽  
B F Samsonov ◽  
B Van den Bossche
Keyword(s):  
Dirac Equation ◽  
Darboux Transformations ◽  
One Dimensional ◽  
The One ◽  
Stationary Dirac Equation

scholarly journals Intertwining technique for the one-dimensional stationary Dirac equation

2003 ◽  
Vol 305 (2) ◽  
pp. 151-189 ◽  
Author(s):  
L.M. Nieto ◽  
A.A. Pecheritsin ◽  
Boris F. Samsonov
Keyword(s):  
Dirac Equation ◽  
One Dimensional ◽  
The One ◽  
Stationary Dirac Equation

DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5807-5822 ◽  
Author(s):  
A. SINHA ◽  
P. ROY
Keyword(s):  
Dirac Equation ◽  
Darboux Transformation ◽  
One Dimensional ◽  
Exactly Solvable ◽  
The One ◽  
Stationary Dirac Equation

The Darboux algorithm is applied to an exactly solvable one-dimensional stationary Dirac equation, with non-Hermitian, pseudoscalar interaction V0(x). This generates a hierarchy of exactly solvable Dirac Hamiltonians, [Formula: see text], defined by new non-Hermitian interactions V1(x), which are also pseudoscalar. It is shown that [Formula: see text] are isospectral to the initial Hamiltonian h0, except for certain missing states.

scholarly journals DARBOUX TRANSFORMATION OF THE GREEN FUNCTION FOR THE DIRAC EQUATION WITH THE GENERAL POTENTIAL

2008 ◽  
Vol 23 (02) ◽  
pp. 247-258 ◽  
Author(s):  
EKATERINA POZDEEVA
Keyword(s):  
Green Function ◽  
Dirac Equation ◽  
Boundary Problem ◽  
Darboux Transformation ◽  
Green Functions ◽  
Regular Boundary ◽  
One Dimensional ◽  
The Green Function ◽  
The One ◽  
Stationary Dirac Equation

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also obtain the formula for the full trace of the difference of the transformed and initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation of the Green function on an interval.

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Ziyatkhan S. Aliyev ◽  
Nazim A. Neymatov ◽  
Humay Sh. Rzayeva
Keyword(s):  
Dirac Equation ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Bifurcation From Infinity ◽  
The One ◽  
Nodal Properties

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

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