Coupling constant dependence for the Schrödinger equation with an inverse-square potential

A. G. Smirnov

We consider the one-dimensional Schrödinger equation $-f^{\prime \prime }+q_{\alpha }f=Ef$ on the positive half-axis with the potential $q_{\alpha }(r)=(\alpha -1/4)r^{-2}$. It is known that the value $\alpha =0$ plays a…