In this talk,I will addressed two problems initialed by E.B.Davies related to higher order Schrodinger operators P(D)+V where P(D) is a general homogeneous constant coefficient elliptic operators of order 2m.One is concerned with the consistence of the maximal and minimal form; another is to obtain the Gaussian upper estimates for the higher order Schrodinger semi -group under the Kato type perturbation.Comparing with second cases,several difficulties exist due to the loss of the positivity and contractivity of unperturbed semigroup.Our methods mainly depend on its analyticity.This is a co-work with Q.Deng and Y.Ding.