Scattering state of Klein-Gordon Particles by q-parameter hyperbolic Poschl-Teller potential
Akpan Ndem Ikot, Hillary P.Obong, Israel O.Owate, Michael C.Onyeaju, and Hassan Hassanabadi
TL;DR
This paper analytically solves the one-dimensional Klein-Gordon equation with a q-parameter hyperbolic Poschl-Teller potential, deriving explicit formulas for scattering and bound states, including reflection, transmission, and energy conditions.
Contribution
It provides exact solutions and explicit expressions for scattering and bound states of Klein-Gordon particles in this specific potential, advancing analytical methods in relativistic quantum mechanics.
Findings
Explicit formulas for reflection and transmission coefficients.
Energy equations for bound states derived.
Solutions expressed in hypergeometric functions.
Abstract
The one-dimensional Klein-Gordon equation for equal vector and scalar q-parameter hyperbolic Poschl-Teller potential is solved in terms of the hypergeometric functions. We calculate in details the solutions of the scattering and bound states. By virtue of the conditions of equation of continuity of the wave functions, we obtained explicit expressions for the reflection and transmission coefficients and energy equation for the bound state solutions
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