Theoretical Proof of and Proposed Experimental Search for the Ground Triplet State of a Wigner-Regime Two-Electron ‘Artificial Atom’ in a Magnetic Field
Marlina Slamet, Viraht Sahni
It is experimentally established that there is no ground triplet state of the natural He 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 exact analytical correlated wave function solution to the equation. The state exists in the Wigner high-electron-correlation regime. 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 same 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.
Axioms•May 3, 2025•1 citation