= Quantum dynamics
<Quantum dynamics> describes the time evolution of a <quantum state> and its observable predictions. For an isolated system with <Hamiltonian operator> $H$, the <Schrödinger equation> is $i\hbar\partial_t|\psi\rangle=H|\psi\rangle$. Equivalently, a <density matrix> satisfies $i\hbar\dot\rho=[H,\rho]$.
For time-independent $H$, the evolution operator is $U(t)=e^{-iHt/\hbar}$. An energy eigenstate changes only by a global phase, whereas a superposition develops relative phases and can display oscillating observables. Interaction with an unobserved environment generally requires <open quantum system> dynamics rather than a unitary evolution for the subsystem alone.
Back to article page
