  We investigate spectral multipliers, Bochner-Riesz means and convergence of
eigenfunction expansion corresponding to the Schr\"odinger operator with
anharmonic potential ${\mathcal L}=-\frac{d^2}{dx^2}+|x|$. We show that the
Bochner-Riesz profile of the operator ${\mathcal L}$ completely coincides with
such profile of the harmonic oscillator ${\mathcal H}=-\frac{d^2}{dx^2}+x^2$.
  It is especially surprising because the Bochner-Riesz profile for the
one-dimensional standard Laplace operator is known to be essentially different
and the case of operators ${\mathcal H}$ and ${\mathcal L}$ resembles more the
profile of multidimensional Laplace operators. Another surprising element of
the main obtained result is the fact that the proof is not based on restriction
type estimates and instead entirely new perspective have to be developed to
obtain the critical exponent for Bochner-Riesz means convergence.
