Construction of the Dirac Equation Central Potential from Phase Shifts and Bound States

1959 ◽  
Vol 113 (1) ◽  
pp. 363-370 ◽  
Author(s):  
Francisco Prats ◽  
John S. Toll
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Phase Shifts ◽  
Central Potential

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

scholarly journals Fermions in the Rindler spacetime

2019 ◽  
Vol 16 (09) ◽  
pp. 1950140 ◽  
Author(s):  
L. C. N. Santos ◽  
C. C. Barros
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Reference Frame ◽  
Bound States ◽  
Liouville Problem ◽  
External Potential ◽  
Compact Expression ◽  
Sturm Liouville

In this paper, we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm–Liouville problem of a Schrödinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.

scholarly journals The relativistic bound states of a non-central potential

Pramana ◽  
2017 ◽  
Vol 88 (4) ◽  
Author(s):  
MAHDI ESHGHI ◽  
HOSSEIN MEHRABAN ◽  
SAMEER M IKHDAIR
Keyword(s):  
Bound States ◽  
Central Potential ◽  
Relativistic Bound States

Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries

2015 ◽  
Vol 70 (9) ◽  
pp. 713-720 ◽  
Author(s):  
Hadi Tokmehdashi ◽  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Linear Potential ◽  
Energy Eigenvalues ◽  
Nu Method

AbstractIn the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation, which describes the motion of a spin-1/2 particle in 1+1 dimensions for mixed scalar–vector–pseudoscalar linear potential are investigated. The Nikiforov–Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms.

Bound states of the Dirac equation outside a hard sphere

1989 ◽  
Vol 192 (2) ◽  
pp. 321-330 ◽  
Author(s):  
R.L Jaffe ◽  
Aneesh Manohar
Keyword(s):  
Dirac Equation ◽  
Hard Sphere ◽  
Bound States

scholarly journals Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Hilmi Yanar ◽  
Ali Havare
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Pseudospin Symmetry ◽  
Molecular Structures ◽  
Centrifugal Term ◽  
Term Energy ◽  
Energy Relations ◽  
Rosen Potential ◽  
Uvarov Method ◽  
Pekeris Approximation

Spin and pseudospin symmetric Dirac spinors and energy relations are obtained by solving the Dirac equation with centrifugal term for a new suggested generalized Manning-Rosen potential which includes the potentials describing the nuclear and molecular structures. To solve the Dirac equation the Nikiforov-Uvarov method is used and also applied the Pekeris approximation to the centrifugal term. Energy eigenvalues for bound states are found numerically in the case of spin and pseudospin symmetry. Besides, the data attained in the present study are compared with the results obtained in the previous studies and it is seen that our data are consistent with the earlier ones.

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