Quantum Particle Dynamics in a Highly Singular 1D-Potential $U(x) = -αδ(x) + βδ'(x)$ Superposed on a Well-Behaved One

We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x) = -αδ(x) + βd(δ(x))/dx$ superposed on a well behaved potential $V(x)$. In this, we construct the full, exact Green's function for such a 1D system analytically in closed form, taking account of a spatially variable mass $m(x)$. Our result shows that there can be no electron transmission through the $βδ'(x)$- potential, regardless of the presence of the $V(x)$- potential and $αδ(x)$, (with $α\ne 0$).

No reviews yet.

No comments yet.