We present a novel approach for solving the time-dependent Schrödinger equation (TDSE). The method we propose converts TDSE to an equivalent Volterra integral equation; introducing global Lagrange interpolation of integrand transforms linear system, which is then solved iteratively. In this paper, derive method, explore its performance on several examples, and discuss corresponding numerical de...

We deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time dependent potential.

We propose an exact controllability result for Schrödinger equations in bounded domains under the Bardos–Lebeau–Rauch geometric control condition with an estimate of the control which is explicit with respect to the time of controllability. Also, we prove an explicit in time logarithmic observability estimate for the Schrödinger equation, where no geometrical conditions are supposed on the domain.

Time-dependent unitary transformations are used to study the Schrödinger equation for explicitly timedependent Hamiltonians of the form H(t) = ~ R(t) · ~ J , where ~ R is an arbitrary real vector-valued function of time and ~ J is the angular momentum operator. The solution of the Schrödinger equation for the most general Hamiltonian of this form is shown to be equivalent to the special case ~ ...

We discuss the observability of a one-dimensional Schrödinger equation on certain time-dependent domain. In linear moving case, we give exact boundary and pointwise internal for arbitrary time. For general moving, provide when curve satisfies some conditions. By duality theory, establish controllability adjoint system.