A Matrix Formalism for the Fock Operator Relative to a Quantum Spherical Non-Parabolic Electron Gas

For the first time, we present a matrix formalism involving the Fock operator relative to a quantum spherical non-parabolic electron gas in the absence of electric and magnetic fields. In fact, a new mathematical physics formulation based on tensor-dyadic product of matrices is proposed for determining the Fock electron energy in a quantum spherical non-parabolic electron gas. In our formulation, phenomenological weight factors are introduced as a measure of electron-electron interaction and electron-confinement effects among other issues.