Abstract: In this paper, the Sch\"odinger uncertainty relation for the unilateral weighted shift operators on Fock space is established, and the explicit expression when the equality attained is given, which further extends the Heisenberg uncertainty relation on Fock space established by Chen Yong and Zhu Kehe in \cite{4} and overcomes the difficulty in \cite{19}. In addition, we generalize the uncertainty relation to the multiple operators case. A new uncertainty inequality in the form of non-self adjoint operators is obtained as well.

Key words: Fock space, Uncertainty Principle, unilateral weighted shift operator, Segal-Bargmann transform, derivation operator