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Quantum particle transmission through locally periodic potentials surroundedby symmetric exterior potentials is analyzed. Closed-form conditions forlocating energy peaks of total transmission are derived. Floquet/Bloch energyband types are defined and found to affect the number of peaks in transmissionbands. Modifications of band types and a band fusion phenomenon are discussed.The theoretical approaches suggested consist of several ways to express aSchr\"{o}dinger wave as an amplitude function multiplying a harmonic functionof a phase function. In particular, an approach containing a Floquet/Blochperiodic amplitude function and a corresponding phase function is described forthe locally periodic region, allowing a way to specify quantum numbers forenergies of total transmission.

Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches