Outline of Lecture

1. Time-dependent Schrödinger equation
   1. Implicit and explicit discretization
   2. 1-D discretization schemes
   3. 2-D Alternate Direction Implicit (ADI)
   4. Variable effective mass
   5. Absorbing boundary conditions
   6. Tight-binding Hamiltonian representation
2. Time-independent transport with Schrödinger equation
   1. 1-D recursion algorithm
   2. Injection boundary conditions for equilibrium contacts: quantum and classical system
   3. Expressions for the current
   4. 1-D transport using transmission line theory
3. 2-D Recursive Green's function in the tight-binding formalism
   1. Decomposition of the 2-D domain
   2. Numerical solution of Dyson's equation in terms of tight-binding Grenn's functions
   3. Transmission and  reflection coefficient
   4. Comparison with mode-matching approach

Background Articles

1.

"Numerical simulaton of mesoscopic systems with open boundaries using the multidimensional time-dependent Schrödinger equation", L.F. Register, U. Ravaioli, and K. Hess, Journal of Applied Physics, vol. 69, pp. 7153-7158, 1991. (720 KB PDF).  "Erratum" (55 KB PDF)

2.

"Theory for a quantum modulated transistor",F. Sols, M. Macucci, U. Ravaioli and K. Hess, Journal of Applied Physics, vol. 66, pp. 3892-3906, 1989. (3.0 MB PDF)

3.

"Quasi 3-D Green's-function simulation of coupled electron waveguides", M. Macucci, A.T. Galick and U. Ravaioli, Physical Review B, vol. 52, pp. 5210-5220 , 1995. (2.8 MB PDF)

Lecture 1

Lab Exercises