文摘
We study the linear fractional Schrödinger equation on a Hilbert space, with a fractional time derivative of order \(0<\alpha <1,\) and a self-adjoint generator A. Using the spectral theorem we prove existence and uniqueness of strong solutions, and we show that the solutions are governed by an operator solution family \(\{ U_{\alpha }(t)\}_{t\ge 0}\). Moreover, we prove that the solution family \(U_{\alpha }(t)\) converges strongly to the family of unitary operators \(e^{-itA},\) as \(\alpha \) approaches to 1.