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.
We present a study of the one-dimensional Klein–Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker Mκ,μ(x) function. The reflection and transmission coefficients are calculated in terms of the energy, the height, and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.
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.
Using the shape invariance approach we obtain exact solutions of one-dimensional Klein–Gordon equation with equal types of scalar and vector hyperbolic Scarf potentials. This is considered in the framework of supersymmetric quantum mechanics method.
We improve previous results on dispersive decay for 1D Klein–Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken the assumption on the potential.
Bound states of a Klein–Gordon particle in the presence of a smooth potential well