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We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthen potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the matching condi
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak elect
Missing bound-state solutions for fermions in the background of a Killingbeck radial potential including an external magnetic and Aharonov-Bohm (AB) flux fields are examined. The correct quadratic form of the Dirac equation with vector and scalar cou
When the Schr{o}dinger equation for stationary states is studied for a system described by a central potential in $n$-dimensional Euclidean space, the radial part of stationary states is an even function of a parameter $lambda$ which is a linear comb
We consider quantum inverse scattering with singular potentials and calculate the Sine-Gordon model effective potential in the laboratory and centre-of-mass frames. The effective potentials are frame dependent but closely resemble the zero-momentum p