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In this paper we investigate the heat kernel of the Schrödinger operatorL  =  -   Δ  G   +  W    $L=-\Delta _G+W$    on the nilpotent Lie group  G , where Δ  G   is the sub-Laplacian on  G  and the non-negative potential  W  belongs to the reverse Hölder class  B   q  1  . The main aim of the paper is to give a pointwise estimate for the heat kernel of Schrödinger operators with non-negative potentials on the nilpotent Lie group  G . As its applications, we obtain the  L p   estimates for parabolic Schrödinger operators with certain non-negative potentials.

An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications