= W. G. Penney
{c}
<W. G. Penney> developed a solvable model of <electrons> in a periodic lattice with <R. de L. Kronig>. Their 1931 calculation replaced the complicated crystal environment by a repeating one-dimensional potential, exposing allowed and forbidden <electron>-<energy> intervals.<Quantum mechanics of electrons in crystal lattices by R. de L. Kronig and W. G. Penney>[Introduction and periodic-potential solution]{ref}
The <Kronig-Penney model> makes <energy bands> concrete: matching <wave functions> across repeated cells constrains the possible energies. Its value lies in isolating the effect of periodicity, not reproducing every interaction in a real solid.
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