An analytic variational wave function is proposed for the ground state of a quasi-one-dimensional electron system as occurring in narrow inversion layers in metal-oxide-semiconductor field-effect-transistor structures. The ground-state energy and the charge density are evaluated as functions of the average channel-electron density and the width of the metal gate by solving Poisson's equation and Schrödinger's equation in the variational self-consistent Hartree approximation.

• Received 28 March 1986

DOI:https://doi.org/10.1103/PhysRevB.33.8874