Theoretical Proof of and Proposed Experimental Search for the Ground Triplet State of a Wigner-Regime Two-Electron ‘Artificial Atom’ in a Magnetic Field
It is experimentally established that there is no ground triplet state of the natural <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>e</mi></mrow></semantics...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/5/349 |
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| Summary: | It is experimentally established that there is no ground triplet state of the natural <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mi>e</mi></mrow></semantics></math></inline-formula> atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot in a magnetic field, as described by the Schrödinger–Pauli equation, we provide theoretical proof of the existence of a ground triplet state by deriving an <i>exact analytical correlated wave function</i> solution to the equation. The state exists in the <i>Wigner high-electron-correlation regime</i>. We further explain that the solution satisfies all requisite symmetry and electron coalescence constraints of a triplet state. Since, due to technological advances, such a Wigner crystal quantum dot can be created, we propose an experimental search for the theoretically predicted ground triplet-state spectral line. We note that there exists an analytical solution to the Schrödinger–Pauli equation for a ground singlet state in the Wigner regime for the <i>same</i> value of the magnetic field. The significance to quantum mechanics of the probable experimental observation of the ground triplet state for an ‘artificial atom’ is discussed. |
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| ISSN: | 2075-1680 |