tpropagation
tpropagation is a term used in some disciplines to denote the propagation of a quantity with respect to a temporal parameter t. It is not a widely standardized term and its precise meaning depends on the context. In physics and applied mathematics, t-propagation often refers to the time evolution of a system: how a state x(t) changes as t increases, governed by a differential equation dx/dt = f(x,t). The solution map, often called the propagator, sends an initial state x(t0) to x(t) for t ≥ t0. In quantum mechanics, the time-evolution operator U(t) = exp(-iHt/ħ) is a concrete realization of t-propagation for states in a Hilbert space.
In wave and field theories, t-propagation describes how wave packets or fields advance in time, subject to
In applied contexts such as signal processing or control theory, t-propagation describes the temporal evolution of
Notation varies; some authors write p(t) or Φ_t to denote the propagating state at time t, while