Wavefunction scaling in a quasi-periodic potential

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Abstract
The nature of wavefunctions in a particular system with two incommensurate periods is discussed. It is shown that the wavefunction can be approximated by a product of functions corresponding to the different quasiperiods, and so these approximate periods serve as discrete length scales for the wavefunction. In this way it can be understood how localised or extended wavefunctions, and also two different types of wavefunctions corresponding to a singular continuous spectrum, can occur. Under certain critical conditions self-similar wavefunctions are found.