Two-Dimensional fully numerical solutions of molecular Schrödinger equations. II. Solution of the Poisson equation and results for singlet states of H2and HeH+

1983 ◽  
Vol 23 (1) ◽  
pp. 319-323 ◽  
Author(s):  
Leif Laaksonen ◽  
Pekka Pyykkö ◽  
Dage Sundholm
Keyword(s):  
Poisson Equation ◽  
Numerical Solutions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
The Poisson Equation ◽  
Singlet States

scholarly journals A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square

2019 ◽  
Vol 53 (3) ◽  
pp. 987-1003 ◽  
Author(s):  
Claudio Canuto ◽  
Ricardo H. Nochetto ◽  
Rob P. Stevenson ◽  
Marco Verani
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
Galerkin Approximation ◽  
Error Reduction ◽  
Two Dimensional ◽  
Dirichlet Problems ◽  
Polynomial Degree ◽  
Unit Square ◽  
The Poisson Equation ◽  
Dimensional Unit

Both practice and analysis of p-FEMs and adaptive hp-FEMs raise the question what increment in the current polynomial degree p guarantees a p-independent reduction of the Galerkin error. We answer this question for the p-FEM in the simplified context of homogeneous Dirichlet problems for the Poisson equation in the two dimensional unit square with polynomial data of degree p. We show that an increment proportional to p yields a p-robust error reduction and provide computational evidence that a constant increment does not.

ANALYTICAL MODELING OF DRAIN CURRENT, CAPACITANCE AND TRANSCONDUCTANCE IN SYMMETRIC DOUBLE-GATE MOSFETs CONSIDERING QUANTUM EFFECTS

2013 ◽  
Vol 12 (01) ◽  
pp. 1350005 ◽  
Author(s):  
VIMALA PALANICHAMY ◽  
N. B. BALAMURUGAN
Keyword(s):  
Numerical Solutions ◽  
Inversion Layer ◽  
Drain Current ◽  
Quantum Effects ◽  
Schrodinger Equations ◽  
Double Gate ◽  
Schrödinger Equations ◽  
Inversion Charge ◽  
Physical Insight ◽  
Quantum Mechanical Effects

An analytical model for double-gate (DG) MOSFETs considering quantum mechanical effects is proposed in this paper. Schrödinger and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum effects (QME) that influence the performance of DG MOSFETs. This model is developed to provide an analytical expression for inversion charge distribution function for all regions of device operation. This expression is used to calculate the other important parameters like inversion layer centroid, inversion charge, gate capacitance, drain current and transconductance. We systematically evaluate and analyze the parameters of DG MOSFETs considering QME. The analytical solutions are simple, accurate and provide good physical insight into the quantization caused by quantum confinement under various gate biases. The analytical results of this model are verified by comparing the data obtained with one-dimensional self-consistent numerical solutions of Poisson and Schrödinger equations known as SCHRED.

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