Triplet State of a Quantum Dot in a Magnetic Field: A 'Quantal-Newtonian' First Law Study

The triplet 2³S state of a two-electron quantum dot in a
magnetic field is studied from the perspective of the 'Quantal
Newtonian' first law. The exact analytical wave function solution
of the corresponding Schrödinger-Pauli equation is derived. The
anti-symmetric nature of the spatial part of the wave function, and
the satisfaction by it of the node electron-electron coalescence
constraint is displayed. The quantal sources of the density,
pair-correlation density, the Fermi-Coulomb hole charge, the
single-particle density matrix, and the current density, and from
these the corresponding Hartree, electron-interaction,
Pauli-Coulomb, Differential Density, Kinetic, and Effective Magnetic
fields are determined. The total energy, and both its external and
internal components are obtained from the various fields. The
intrinsic self-consistent nature of the Schrödinger-Pauli
equation, and thereby the satisfaction of the 'Quantal Newtonian'
first law is shown.