dorsal/arxiv
View SchemaAn Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential
| Authors | Athanasios N. Petridis, Lawrence P. Staunton, Jon Vermedahl, Marshall Luban |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403177 |
| URL | https://arxiv.org/abs/quant-ph/0403177 |
Abstract
Analytical solutions to the time-dependent Shr\"{o}dinger 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.
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"abstract": "Analytical solutions to the time-dependent Shr\\\"{o}dinger equation in one\ndimension are developed for time-independent potentials, one consisting of an\ninfinite wall and a repulsive delta function. An exact solution is obtained by\nmeans of a convolution of time-independent solutions spanning the given Hilbert\nspace with appropriately chosen spectral functions. Square-integrability and\nthe boundary conditions are satisfied. The probability for the particle to be\nfound inside the potential well is calculated and shown to exhibit\nnon-exponential decay decreasing at large times as $t^{-3}$. The result is\ngeneralized for all square-integrable solutions to this problem.",
"arxiv_id": "quant-ph/0403177",
"authors": [
"Athanasios N. Petridis",
"Lawrence P. Staunton",
"Jon Vermedahl",
"Marshall Luban"
],
"categories": [
"quant-ph"
],
"title": "An Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential",
"url": "https://arxiv.org/abs/quant-ph/0403177"
},
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"type": "Model",
"variant": "snapshot-2026-03-01",
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