A special initial value problem for the operator-valued Riccati differential equation (RDE) is used for studying section determinants of unitary operators. A solvability criterion for this initial value problem is derived by providing an a-priori estimate of the solution. Alternatively, the same estimate is derived by a method that is based entirely upon linear algebra.

Section determinants, unitary operators, time-dependent Schrödinger equation, operator Riccati differential equation, a-priori estimate

34G20 (34G10)