When a quantum particle interacts with time-dependent forces, exact solutions are rare. One of the simplest solvable cases is a one-dimensional particle driven by a spatially uniform, time-dependent external force. This piece offers a concise overview of the problem.

The reduced density operator is a fundamental concept in quantum mechanics, enabling the description of a subsystem by tracing out the degrees of freedom of the rest of the system. This brief overview revisits its definition and derives its key properties.

Numerically solving the time-dependent Schrödinger equation can be approached in several ways. In this overview, we present an efficient method based on the Chebyshev polynomial expansion of the time-evolution operator.