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Fractional wave-function revivals in the infinite square well

David L. Aronstein and C. R. Stroud, Jr.

Phys. Rev. A 55, 4526 (1997).

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.

Click here to download the original .pdf version of the paper aronstein971.pdf (245 KB)
(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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