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Two connected equiperiodic one-dimensional multi-well potentials of differentwell depths are studied. Floquet/Bloch energy bands for respective multi-wellpotential are found to be relevant for understanding level structures. Althougenergies are classically allowed in both multi-well potentials, a band gap ofone multi-well potential makes this potential quantum-mechanically 'forbidden'.All energy levels are located in the union of the band regions.

On quantum bound states in equiperiodic multi-well potentials I: $-$ Locally periodic potential sequences and Floquet/Bloch bands