Test of a variational method applied to disordered systems

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Abstract
The density of states of a particle interacting with a simple model of a structurally disordered system is calcualted as the first test of a new approach. The chosen model can be solved exactly and constitutes a harsh test of the new and more conventional methods. The new approach consists in applying a variational procedure to the calculation of the partition function of the system. Using a wide range of model parameters, it is found that the variational method yields results which are an improvement over those of conventional methods and which are exact in all extreme cases. Particular attention is given to an intermediate range of model parameters in order to exhibit clearly the shortcomings of the method.