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## Main Question or Discussion Point

Say we start with a wavefunction inside a harmonic potential well, such that the initial ##\psi(x)## is confined to a central region much smaller than the ground state (hence ##V(x)\approx0##).. and the expectation Kinetic Energy is equal to an energy eignenvalue ##E_n## of the system.

Starting from here, will it ultimately converge over time into an energy eigenstate corresponding to ##E_n## ... OR.. will it slosh around forever in a complicated way?

Starting from here, will it ultimately converge over time into an energy eigenstate corresponding to ##E_n## ... OR.. will it slosh around forever in a complicated way?