Journal of the
Korean Mathematical Society JKMS

The unitary Lie--Trotter--Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schr\"odinger equation. In this note we want to survey some of recent results on the {\it norm convergence} of the selfadjoint Lie--Trotter-Kato product formula for the Schr\"odinger operator $- \frac{1}{2}\Delta + V(x)$ and for the sum of two selfadjoint operators $A$ and $B$. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schr\"odinger equation.

Keywords: Lie--Trotter--Kato product formula, Schrodinger operator, semigroup

MSC numbers: 47D06, 35J10, 60J65, 81Q10