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A general analysis of scattering in finitely periodic one-dimensional potentials is considered. Using a previously developed method of potential segmentation, the authors factor out exactly the effect due to the period multiplicity via polynomials which are insensitive to the shape of a generic potential cycle and correlate the transmission resonances with the zeros of these polynomials. In the limit of infinite period multiplicity, the standard results of band structure are regained. Numerical examples are given to illustrate applicability to potentials of arbitrary shape.

Spatial geometry of the rotating disk and its non-rotating counterpart Am. J. Phys. 80, 772 (2012) On energy transfers in reflection of light by a moving mirror Am. J. Phys. 80, 684 (2012) A general principle for light reflecting from a uniformly moving mirror: A relativistic treatment Am. J. Phys. 80, 680 (2012) Geometric diagram for relativistic addition of velocities Am. J. Phys. 80, 737 (2012) Fizeau's "aether-drag" experiment in the undergraduate laboratory Am.

An alternative approach to the one-dimensional scattering problem is presented in which the potential is replaced by a sequence of flat barriers or wells. The resulting problem is solved exactly and the transmission coefficient obtained via multiplication of a string of 2×2 matrices.

This paper gives the results of a variational calculation using a 100-term wavefunction on the ground (para) state of (P-I'-p)+, including the effects of the finite proton mass. The energy found is sensitive to the muon mass; with mil = 206�77 me, we find (B.E.)PIIP to be 253�14�0�01 eV. Results are also given for the muon-proton overlap, and for a number of other geometric averages of the wavefunction