Modified Schrodinger-Poisson equation: Quantum polytropes

Schrodinger Equation and Quantum Chemistry

A Poisson formula for the Schrodinger operator

We prove a nonlinear Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous paper by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover,...

Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson-Boltzmann equation which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concent...

Self-Consistent Solution of the Schrodinger and Poisson Equations Applied to Quantum Well Heterostructures

A novel numerical approach to solving Schr odinger's equation as applied to quantum well heterostructures is described. The quantum mechanical energy subbands, wave functions and charge density are calculated based on a two-directional fourthorder Runge-Kutta (RK4) algorithm. The algorithm is applied to well-de ned quantum well structures. Results are compared with analytic solutions to ensure...

A Stable Schrodinger-Poisson Solver to Investigate Quantum Effects in Modem M OSFETs

As a consequence of continuous scaling of MOS devices and the resulting high transverse electric fields at the interface, a reliable device simulation tool has to account for the quantized states in the channel. From a methodological point of view it seems favorable for the simulation of complete devices to consider the quantization effects by onedimensional cuts perpendicular to the interface ...