Image method solutions for free-particle wave packets in wedge geometries

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Using analogues of familiar image methods in electrostatics and optics, we show how to construct closed-form wave packet solutions of the two-dimensional free-particle Schrödinger equation in geometries restricted by two infinite wall barriers separated by an angle ΘN ≤ π/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a Θ3 ≤ π/3 ≤ 60° wedge. We review the time development of zero-momentum wave packets placed near a single infinite wall barrier in the appendix.

Original languageEnglish (US)
Pages (from-to)281-289
Number of pages9
JournalEuropean Journal of Physics
Volume27
Issue number2
DOIs
StatePublished - Mar 1 2006

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wave packets
wedges
geometry
momentum
optics
analogs
electrostatics

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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abstract = "Using analogues of familiar image methods in electrostatics and optics, we show how to construct closed-form wave packet solutions of the two-dimensional free-particle Schr{\"o}dinger equation in geometries restricted by two infinite wall barriers separated by an angle ΘN ≤ π/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a Θ3 ≤ π/3 ≤ 60° wedge. We review the time development of zero-momentum wave packets placed near a single infinite wall barrier in the appendix.",
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Image method solutions for free-particle wave packets in wedge geometries. / Robinett, Richard Wallace.

In: European Journal of Physics, Vol. 27, No. 2, 01.03.2006, p. 281-289.

Research output: Contribution to journalArticle

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N2 - Using analogues of familiar image methods in electrostatics and optics, we show how to construct closed-form wave packet solutions of the two-dimensional free-particle Schrödinger equation in geometries restricted by two infinite wall barriers separated by an angle ΘN ≤ π/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a Θ3 ≤ π/3 ≤ 60° wedge. We review the time development of zero-momentum wave packets placed near a single infinite wall barrier in the appendix.

AB - Using analogues of familiar image methods in electrostatics and optics, we show how to construct closed-form wave packet solutions of the two-dimensional free-particle Schrödinger equation in geometries restricted by two infinite wall barriers separated by an angle ΘN ≤ π/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a Θ3 ≤ π/3 ≤ 60° wedge. We review the time development of zero-momentum wave packets placed near a single infinite wall barrier in the appendix.

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