Quantum Theory on a Network. II. A Solvable Model Which May Have Several Bound States per Node Point

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Abstract
This is a further development of a network model for electrons in solids. It is postulated that the electrons are restricted to move along 1‐dimensional lines between atoms. The network for a given solid corresponds to that which one would use in a wire and ball model to exhibit the crystal structure. A potential of the form V = −V0 sech2γx is associated with each ``atomic'' node point. The atom can have 1, 2, 3, or more electronic bound states, depending on V0 and γ. The wavefunctions have the usual Bloch form and involve hypergeometric functions. The density of states is plotted. Localized defect energy levels are also given for various types of atomic defects. An especially interesting feature of the model is that all the above‐mentioned calculations are made exactly, without resorting to perturbation theory.

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