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<p>In this work, we investigate electron energy spectra and localization in a three-dimensional harmonium system using the shifted 1/N-expansion method. Our results show that increasing confinement strength <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\upomega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">ω</mi> </math></EquationSource> </InlineEquation> raises energy levels and reduces equilibrium interelectron distances, as stronger confinement forces electrons into tighter spatial regions. In the strong-correlation limit <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\upomega \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">ω</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, we confirm the formation of a Wigner molecule. Additionally, we establish the transition from the Wigner molecule regime to a strongly confined state where quantum confinement suppresses correlation effects. Our results further show that energy levels increase by increasing the principal quantum number (n), while centrifugal effects lead to a slight reduction in energy levels with increasing angular momentum number (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ℓ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. These results enhance our understanding of electron correlation effects in confined quantum systems and have potential applications in nanophysics and quantum computing.</p>

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A Theoretical Study of Wigner Molecule Formation in Strongly Correlated Three-Dimensional Harmonium

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Mohammad A. Dalabeeh,
  • Ayman S. Sandouqa,
  • Omar T. Al-Obeidat,
  • Amal F. Al-Maaitah,
  • Mustafa M. Hawamdeh

摘要

In this work, we investigate electron energy spectra and localization in a three-dimensional harmonium system using the shifted 1/N-expansion method. Our results show that increasing confinement strength \(\upomega \) ω raises energy levels and reduces equilibrium interelectron distances, as stronger confinement forces electrons into tighter spatial regions. In the strong-correlation limit \(\upomega \rightarrow 0\) ω → 0 , we confirm the formation of a Wigner molecule. Additionally, we establish the transition from the Wigner molecule regime to a strongly confined state where quantum confinement suppresses correlation effects. Our results further show that energy levels increase by increasing the principal quantum number (n), while centrifugal effects lead to a slight reduction in energy levels with increasing angular momentum number ( \(\ell )\) ℓ ) . These results enhance our understanding of electron correlation effects in confined quantum systems and have potential applications in nanophysics and quantum computing.