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Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

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Abstract

For the first time we introduce an operator Δ h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 κ κ 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution.

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Authors and Affiliations

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai, 200030, China

    Qin Guo & Hong-Yi Fan

  2. Department of Physics, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China

    Qin Guo

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  1. Qin Guo
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  2. Hong-Yi Fan
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Correspondence to Qin Guo.

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Work supported by the National Natural Science Foundation under the grant: 10775097.

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Guo, Q., Fan, HY. Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation. Int J Theor Phys 47, 3234–3247 (2008). https://doi.org/10.1007/s10773-008-9759-1

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  • DOI: https://doi.org/10.1007/s10773-008-9759-1

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