Scattering in quantum mechanics under quaternionic Dirac delta potential

2016 ◽  
Vol 94 (3) ◽  
pp. 262-266 ◽  
Author(s):  
Hadi Sobhani ◽  
Hasan Hassanabadi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Reflection And Transmission ◽  
Dirac Delta ◽  
Transmission Coefficients ◽  
Delta Potential ◽  
Quaternionic Quantum Mechanics ◽  
Derivative Discontinuity ◽  
Current Densities ◽  
Dirac Delta Potential

In this paper, the Schrödinger equation for quaternionic quantum mechanics with a Dirac delta potential has been investigated. The derivative discontinuity condition for the quaternionic wave function has been derived and the boundary conditions for the quaternionic wave function have been applied. Probability current densities for different regions of the problem have been determined along with reflection and transmission coefficients.

scholarly journals Scattering Study of Fermions due to Double Dirac Delta Potential in Quaternionic Relativistic Quantum Mechanics

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Hassan Hassanabadi ◽  
Hadi Sobhani ◽  
Won Sang Chung
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Scattering Problem ◽  
Relativistic Quantum Mechanics ◽  
Dirac Delta ◽  
Transmission Coefficients ◽  
Delta Potential ◽  
Vector Potentials ◽  
Scattering Study ◽  
Dirac Delta Potential

We have studied the scattering problem of relativistic fermions from a quaternionic double Dirac delta potential. We have used Dirac equation in the presence of the scalar and vector potentials in the quaternionic formalism of relativistic quantum mechanics to study the problem. The wave functions of different regions have been derived. Then, using the reflection coefficient, transmission coefficient, and the continuity equation, the scattering problem has been investigated in detail. It has been shown that we have faced some fluctuations in the reflection and transmission coefficients.

scholarly journals Angular invariant quantum mechanics in arbitrary dimension

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Sergio Giardino
Keyword(s):  
Quantum Mechanics ◽  
Arbitrary Dimension ◽  
Free Particle ◽  
Whittaker Functions ◽  
One Dimensional ◽  
Dirac Delta ◽  
Finite Barrier ◽  
Dirac Delta Potential ◽  
Invariant Quantum ◽  
Infinite Potential Well

One dimensional quantum mechanics problems, namely the infinite potential well, the harmonic oscillator, the free particle, the Dirac delta potential, the finite well and the finite barrier are generalized for finite arbitrary dimension in a radially symmetric, or angular invariant, manner. This generalization enables the Schrödinger equation solutions to be visualized for Bessel functions and Whittaker functions, and it also enables connections to multi-dimensional physics theories, like string theory.

scholarly journals q-Deformed Relativistic Fermion Scattering

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hadi Sobhani ◽  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Quantum ◽  
Reflection And Transmission Coefficients ◽  
Relativistic Quantum Mechanics ◽  
Scattering Problems ◽  
Reflection And Transmission ◽  
Transmission Coefficients

In this article, after introducing a kind ofq-deformation in quantum mechanics, first,q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then, three important scattering problems in physics are studied. All results have satisfied what we had expected before. Furthermore, effects of all parameters in the problems on the reflection and transmission coefficients are calculated and shown graphically.

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