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Summer School on Computational Materials Science
2002
University of Illinois, Urbana-Champaign

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Schrödinger-Poisson Solvers Description and Quantum Corrections in Classical Simulators

Dragica Vasileska - vasilesk@imap2.asu.edu

Department of Electrical Engineering

Arizona State University

Outline of Lecture

  1. Schrödinger-Poisson solvers
    1. Major concerns for future integrated circuits
    2. Time-dependent Schrödinger wave equation
    3. Discretization for variable effective mass
    4. Time-independent Schrödinger equation
    5. Airy function method
    6. Variational approach
    7. Shooting method for 1D problem - SCHRED program description
    8. Finding the roots of a characteristic polynomial
    9. The Lanczos algorithm
    10. Numerov algorithm
    11. 2D and 3D eigenvalue solvers
    12. Open systems
  2. The effective potential approach
    1. Madelung and Bohm's reformulation of quantum mechanics
    2. Other quantum potential formulations
    3. Effective potential approach due to Ferry
    4. Simulation examples
    5. Conclusions
 
   

Lecture 1

Schrödinger Poisson Solvers Description and Quantum Corrections in Classical Simulation
  Presentation - download (503 KB PDF)

Lab Exercises

  Exercises with the SCHRED program (76 KB PDF)

 

Last Updated August 13, 2002
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