Analytical solution of the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials: Universal three-body parameter of mixed-dimensional Efimov states

Yuki Ohishi, Kazuki Oi, Shimpei Endo

We study the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive…