An electron moves in a one-dimensional lattice with the separation between adjacent atoms being equal to a.
a. Write down the momentum eigenvalue equation for the electron.
b. Find the general form of the solutions of the eigenvalue equation.
c. By requiring that the eletonr's wave function psi(x) statisfies the periodic boundary condition,
psi(a) = psi(0),
determine the possible values of the momentum of the electron.
p = -ih d/dx
The Attempt at a Solution
So my question is less at being stuck on solving the problem and more of not understanding the question. I do not understand how to deal with a one-dimensional lattice in which an electron moves--my text does not talk about it whatsoever. Am I supposed to treat the electron as in some sort of finite well with width a? I really do not understand how to interpret this idea of a lattice, and thus, cannot even make an attempt at the problem.
Thanks for the help!
Note: this course is introductory quantum, I'm taking proper quantum next year. So we don't use matrices or linear vector spaces, etc. Our notion of an operator is confined to operator x function = constant x function. Sorry if this belongs in the introductory forum--I wasn't sure where to put it.