Fractional wave-function revivals in the infinite square well
David L. Aronstein and C. R. Stroud, Jr.
Phys. Rev. A 55, 4526 (1997).
Click here to download the original .pdf version of the paper
aronstein971.pdf (245 KB)
We describe the time evolution of a wavefunction in the infinite square
well using a fractional revival formalism and show that at all times the
wavefunction can be described as a superposition of translated copies of
the initial wavefunction. Using the model of a waveform propagating on a
dispersionless string from classical mechanics to describe these
translations, we connect the reflection symmetry of the square well
potential to a reflection symmetry in the locations of these translated
copies and show that they occur in a "parity-conserving" form. The
relative phases of the translated copies are shown to depend quadratically
on the translation distance along the classical path. We conclude that the
time-evolved wavefunction in the infinite square well can be described in
terms of translations of the initial wavefunction shape, without
approximation and without any reference to its energy eigenstate expansion.
That is, the set of translated initial wavefunctions forms a Hilbert space
basis for the time-evolved wavefunctions.
(Original version that appeared in Phys. Rev. A.)
Click here to download the revised .pdf version of the paper
aronstein971v2.pdf (840 KB)
(Improved figures and typos corrected)
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