One-dimensional quantum scattering by a parabolic odd potential
arXiv:1401.6313 · doi:10.1088/1751-8113/45/41/415302
Abstract
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schrödinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A complete discussion of the scattering function reveals the existence of Gamow (decaying) states and of resonances.
14 pages, 7 figures