dorsal/arxiv
View SchemaWigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets
| Authors | M. Belloni, M. A. Doncheski, R. W. Robinett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312086 |
| URL | https://arxiv.org/abs/quant-ph/0312086 |
| DOI | 10.1119/1.1767100 |
Abstract
We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time.
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"abstract": "We calculate the Wigner quasi-probability distribution for position and\nmomentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite\nwell potential, using both x- and p-space stationary-state solutions, as well\nas visualizing the results. We then evaluate the time-dependent Wigner\ndistribution, P_W(x,p;t), for Gaussian wave packet solutions of this system,\nillustrating both the short-term semi-classical time dependence, as well as\nlonger-term revival and fractional revival behavior and the structure during\nthe collapsed state. This tool provides an excellent way of demonstrating the\npatterns of highly correlated Schrodinger-cat-like `mini-packets\u0027 which appear\nat fractional multiples of the exact revival time.",
"arxiv_id": "quant-ph/0312086",
"authors": [
"M. Belloni",
"M. A. Doncheski",
"R. W. Robinett"
],
"categories": [
"quant-ph"
],
"doi": "10.1119/1.1767100",
"title": "Wigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets",
"url": "https://arxiv.org/abs/quant-ph/0312086"
},
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