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The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-independent Hamiltonians, the time evolution operator is simply exp(-iHt).

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Time dependence of wave packets without eigenfunctions

In general, to obtain the time dependence of an arbitrary wave packet $\left| \phi(x)\right>$ in the Schödinger picture, we expand the wave packet in the energy eigenfunction basis $\left| \psi_n(x)\r …
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