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