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Foil 4 Quantum Physics and Examples of Use of Computation

From CPS615-Physical Simulation Techniques and Structure of CFD Equations Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 14 November 96. by Geoffrey C. Fox *
Secs 313.9
1 This is a fundamental description of the microscopic world. You would in principle use it to describe everything but this is both unnecessary and too difficult both computationally and analytically.
2 Quantum Physics problems are typified by Quantum Chromodynamics (QCD) calculations and these end up looking identical to statistical physics problems numerically. There are also some chemistry problems where quantum effects are important. These give rise to several types of algorithms.
  • Solution to Schrodinger's equation (a partial differential equation). This can only be done exactly for simple 2-->4 particle systems
  • Formulation of a large matrix whose rows and columns are the distinct states of the system. This is followed by typical matrix operations (diagonalization, multiplication, inversion)
  • Statistical methods which can be thought of as Monte Carlo evaluation of integrals gotten in integral equation formulation of problem
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