An Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential

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dc.creatorPetridis, Athanasios N.
dc.creatorStaunton, Lawrence P.
dc.creatorVermedahl, Jon
dc.creatorLuban, Marshall
dc.date2004-03-24
dc.date.accessioned2026-07-07T06:09:23Z
dc.date.available2026-07-07T06:09:23Z
dc.descriptionAnalytical solutions to the time-dependent Shrödinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of a convolution of time-independent solutions spanning the given Hilbert space with appropriately chosen spectral functions. Square-integrability and the boundary conditions are satisfied. The probability for the particle to be found inside the potential well is calculated and shown to exhibit non-exponential decay decreasing at large times as $t^{-3}$. The result is generalized for all square-integrable solutions to this problem.
dc.description12 pages, including 4 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0403177
dc.identifierhttp://arxiv.org/abs/quant-ph/0403177
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91941
dc.subjectQuantum Physics
dc.titleAn Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential
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