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

R. W. Robinett

doi:10.1088/0143-0807/27/2/011

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

R. W. Robinett

Physics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 Θ_N ≤ 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 language	English (US)
Pages (from-to)	281-289
Number of pages	9
Journal	European Journal of Physics
Volume	27
Issue number	2
DOIs	https://doi.org/10.1088/0143-0807/27/2/011
State	Published - Mar 1 2006

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1088/0143-0807/27/2/011

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title = "Image method solutions for free-particle wave packets in wedge geometries",

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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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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JO - European Journal of Physics

JF - European Journal of Physics

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

Abstract

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