  The analytic form of the electrostatic potential felt by a slowly moving test
charge in quantum plasma is being derived. It has been shown that the potential
composed of two parts: Debye-Huckel screening term and near-field wake
potential which depends on the velocity of the test charge and the number
density of the plasma electrons. Rayleigh-Ritz variational calculation has been
done to estimate precise energy eigenvalues of hydrogen-like ion under such
plasma environment. A detailed analysis shows that the energy levels are
gradually moves to the continuum with increasing plasma electron density while
level crossing phenomenon have been observed with the variation of ion
velocity.
