The Recursion Method and the Schroedinger Equation
The use of generalized orthogonal polynomials is described for the calculation of quantum mechanical properties of physical systems. Quantum mechanics and its mathematical representation are reviewed. Expressions for various physical quantities are related to the orthogonal polynomials obtained from the action of an observable on particular states. Polynomial sets for which weight distributions are known may be used as exact models form which the solutions of other models may be approximated by perturbations. The finite precision, orthogonal polynomial can be constructed numerically even for infinite dimensional models.
KeywordsStationary State Orthogonal Polynomial Continue Fraction Wave Mechanic Random Potential
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