Quantum Particle Dynamics in a Highly Singular 1D-Potential $U(x)=-\alpha \delta (x)+\beta {\delta }^{\prime }(x)$ Superposed on a Well-Behaved One

Norman J. Morgenstern Horing

We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x)=-\alpha \delta (x)+\beta d(\delta (x))/dx$ superposed…