  We show how to derive fixed-point Hamiltonians in quantum mechanics from a
proposed renormalization group invariance approach that relies in a subtraction
procedure at a given energy scale. The scheme is valid for arbitrary
interactions that originally contain point-like singularities (as the
Dirac-delta and/or its derivatives). One example of diagonalization of a
fixed-point Hamiltonian illustrates the procedure for an interaction that
contains regular and singular parts. In another example, the fixed point
Hamiltonian is derived for the case of higher order singularities in the
interaction.
