Quantum · undergrad

Time Evolution Operator

The unitary operator that advances a quantum state in time.

Published Apr 26, 2026 · 1 min

PDF View

The PDF file is linked, but it has not been added yet.

/sources/time-evolution-operator.pdf

Time-Independent Hamiltonian

If $H$ is time independent,

U(t)=e^{-iHt/\hbar}.

The state evolves as

|\psi(t)\rangle = U(t)|\psi(0)\rangle.

Unitarity preserves normalization.

The noncommutativity measure that organizes quantum observables.

The master equation governing the time evolution of the wavefunction.

The total probability associated with a quantum state must equal one.