Proper quantization rule approach to three-dimensional quantum dots

Fernando Adan Serrano; Shi Hai Dong

doi:10.1002/qua.24449

Proper quantization rule approach to three-dimensional quantum dots

Fernando Adan Serrano, Shi Hai Dong

Research output: Contribution to journal › Review article › peer-review

11 Scopus citations

Abstract

In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius r_C by the proper quantization rule and the Wentzel-Kramers-Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius r_C in three dimensions.

Original language	English
Pages (from-to)	2282-2286
Number of pages	5
Journal	International Journal of Quantum Chemistry
Volume	113
Issue number	20
DOIs	https://doi.org/10.1002/qua.24449
State	Published - 15 Oct 2013

Keywords

Wentzel-Kramers- Brillouin
bound states
proper quantization rule
quantum dots

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10.1002/qua.24449

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abstract = "In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius rC by the proper quantization rule and the Wentzel-Kramers-Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius rC in three dimensions.",

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AB - In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius rC by the proper quantization rule and the Wentzel-Kramers-Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius rC in three dimensions.

KW - Wentzel-Kramers- Brillouin

KW - bound states

KW - proper quantization rule

KW - quantum dots

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JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

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ER -

Proper quantization rule approach to three-dimensional quantum dots

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