  We construct (assuming the quantum inverse scattering problem has a solution
) the operator that yields the zeroes of the Riemman zeta function by defining
explicitly the supersymmetric quantum mechanical model (SUSY QM) associated
with the p-adic stochastic dynamics of a particle undergoing a Brownian random
walk . The zig-zagging occurs after collisions with an infinite array of
scattering centers that fluctuate randomly. Arguments are given to show that
this physical system can be modeled as the scattering of the particle about the
infinite locations of the prime numbers positions. We are able then to
reformulate such p-adic stochastic process, that has an underlying hidden
Parisi-Sourlas supersymmetry, as the effective motion of a particle in a
potential which can be expanded in terms of an infinite collection of p-adic
harmonic oscillators with fundamental (Wick-rotated imaginary) frequencies
$\omega_p = i log~p$ (p is a prime) and whose harmonics are $\omega_{p, n} = i
log ~ p^n$. The p-adic harmonic oscillator potential allow us to determine a
one-to-one correspondence between the amplitudes of oscillations $a_n$ (and
phases) with the imaginary parts of the zeroes of zeta $\lambda_n$, after
solving the inverse scattering problem.
