Complex Eigenvalues of the Parabolic Potential Barrier and Gel'fand Triplet

Toshiki Shimbori, Tsunehiro Kobayashi

The paper deals with the one-dimensional parabolic potential barrier $V(x)=V_0-m{\gamma }^2{x}^2/2$, as a model of an unstable system in quantum mechanics. The time-independent Schrödinge…