scholarly journals Klein Paradox for Bound States - a Puzzling Phenomenon

2006 ◽  
Vol 5 (2) ◽  
pp. 14-18
Author(s):  
Nagalakshmi A. Rao ◽  
B. A. Kagali
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Minimal Coupling ◽  
Paradoxical Situation ◽  
Coupling Procedure ◽  
The Hill ◽  
Relativistic Particles

While Klien paradox is often encountered in the context of scattering of relativistic particles at a potential barrier,we presently discuss a puzzling situation that arises with the Klien-Gordon equation for bound states. With the usual minimal coupling procedure of introducing the interaction potential, a paradoxical situation results when the "hill" becomes a "well" ,simulating a bound state like situation.This phenomenal phenomenon for bound states is contrary to the convectional wisdom of quantum mechanics and is analogous to the well-known Klien paradox,a generic property of relativistic wave equation.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Instability of charged massive scalar fields in bound states around Kerr–Sen black holes

2015 ◽  
Vol 24 (14) ◽  
pp. 1550102 ◽  
Author(s):  
Haryanto M. Siahaan
Keyword(s):  
Black Holes ◽  
Bound States ◽  
Gordon Equation ◽  
Scalar Fields ◽  
Bound State ◽  
Imaginary Component ◽  
Scalar Perturbation ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Klein Gordon

In this paper, we show the instability of a charged massive scalar field in bound states around Kerr–Sen black holes. By matching the near and far region solutions of the radial part in the corresponding Klein–Gordon equation, one can show that the frequency of bound state scalar fields contains an imaginary component which gives rise to an amplification factor for the fields. Hence, the unstable modes for a charged and massive scalar perturbation in Kerr–Sen background can be shown.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

scholarly journals Generalized relativistic wave equations with intrinsic maximum momentum

2014 ◽  
Vol 29 (15) ◽  
pp. 1450080 ◽  
Author(s):  
Chee Leong Ching ◽  
Wei Khim Ng
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Scalar Potential ◽  
Bound State ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Relativistic Wave ◽  
One Dimensional ◽  
Nonperturbative Effect ◽  
Klein Gordon

We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein–Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.

scholarly journals Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Gordon Equation ◽  
Free Particle ◽  
Space Time ◽  
Spinless Particle ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Rindler Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.

scholarly journals EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN–GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL

2008 ◽  
Vol 19 (09) ◽  
pp. 1425-1442 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Exact Bound ◽  
Pseudoharmonic Potential ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Klein Gordon Equation

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

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