  For the PT symmetric potential of Dorey, Dunning and Tateo we show that in
the large angular momentum (i.e., strongly spiked) limit the low-lying
eigenstates of this popular non-Hermitian problem coincide with the shifted
Hermitian harmonic oscillators calculated at the zero angular momentum. This
type of an approximate Hermitization is valid in all the domain where the
spectrum of energies remains real. It proves very efficient numerically. The
construction is asymmetric with respect to the sign of the subdominant
square-root spike, and exhibits a discontinuity at the point where the PT
symmetric regularization vanishes.
