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In this and in a following paper the localization problem in real disordered systems is considered from first principles with the help of the recursion method. A Hermitian representation of the Hamilton matrix is given. The concept of the extended Hilbert space is introduced in order to find a convenient representation of the recursion method which allows us to handle the localization problem. For systems containing only nearest neighbour interactions a new useful approximation for the vector system is given within which the Hamiltonian is tridiagonal. The influence of the degree of disorder on the energy spectrum of a semi‐infinite “partially disordered chain” is studied.

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