Electronic Levels of a Model of Liquid Potassium

As a one-dimensional model of a liquid a chain of atoms is considered in which the distances of nearest neighbours are independent random variables having a given probability distribution. Electronic levels are derived using the tight binding approximation. The distribution of quantum states on the energy scale is obtained by applying known results from the mathematics of Jacobian matrices. Using atomic fields appropriate to the potassium atom it is shown that the conducting property of potassium and the insulating property of argon are preserved in the liquid state and that the band structure of the solid state is not essentially changed by the transition from the ordered to the disordered atomic structure.