  Color screening and parton inelastic scattering modify the heavy-quark
antiquark potential in the medium that consists of particles from quantum
chromodynamics (QCD), leading to suppression of quarkonium production in
relativistic heavy-ion collisions. Due to small charm/anti-charm ($c\bar{c}$)
pair production number in proton-nucleus (pA) collisions, the correlation
between different $c\bar{c}$ pairs is negligible, which makes the Schr\"odinger
equation viable for tracking the evolution of only one $c\bar{c}$ pair. We
employ the time-dependent Schr\"odinger equation with in-medium $c\bar{c}$
potential to study the evolution of charmonium wave functions in the
hydrodynamic like QCD medium produced in pA collisions. We explore different
parametrizations of real and imaginary parts of $c\bar{c}$ potential and
calculate the nuclear modification factors ($R_{\rm pA}$) of $J/\psi$ and
$\psi(2S)$ in $\sqrt{s_{NN}}=5.02$ TeV energy p-Pb collisions at Large Hadron
Collider (LHC). Comparing a strong and a weak screening scenario with
experimental data in this approach, we arrive at the conclusion that the color
screening is weak at temperature close to deconfined phase transition.
Moreover, the imaginary part of the potential is crucial to describe the
experimental data which is consistent with widely studied semi-classical
approaches where the dissociation rates are essential.
