  We discuss the nature of pressure induced phase transitions in standard
Quantum Paraelectrics near quantum critical point. From a microscopic theory we
first show that near the critical point the transition temperature $T_c(p)$
varies as $ (1-p/p_c)^\xi$ with $\xi={1/2}$. Within the Landau scheme, it is
shown that for $\xi \leq 1$, a condition satisfied by most quantum
paraelectrics the transition is inevitably first order in nature. The present
analysis is valid for non-polar impurity induced transitions in these materials
and is supported by some recent experiment.
