Exact Results in Quantum Theory

In quantum mechanics potential -g/r^2 is singular if the coupling constant g is too big. Therefore, to define a system with such a potential one needs to renormalize. I will present a simple application of a renormalization group procedure to the problem. As a result, we obtain a family of effective Hamiltonians which depend on the floating cutoff parameter. The family of Hamiltonians exhibits a rich structure with limit cycles, fixed points,triviality and asymptotic-freedom-like behaviors. I will also comment on more popular approaches to renormalization of 1/r^2 potential and argue the value of our approach.