On the trace norm estimate of the Trotter product formula for Schrödinger operators (Q1268684)

The author establishes a formula for the rate of convergence for the Trotter product formula for the Schrödinger operator \((-1/2)\Delta +V\) in the space \(L_2(\mathbb{R}^d)\) as \(t \rightarrow +0\). The nonnegative continuous potential \(V\) satisfies some general conditions. The estimate is given in the trace norm of the operator. The paper follows the lines of \textit{A. Doumeki}, \textit{T. Ichinose} and \textit{H. Tamura} [J. Math. Soc. Japan 50, 359-377 (1998; Zbl 0910.47031)] and presents more sharp bounds.