Presents an analytical theory of the electronic states in ideal
low-dimensional systems and finite crystals based on a theory of
differential equations approach
Demonstrates that the existence of the boundary-dependent states is a
fundamental distinction of the quantum confinement of Bloch waves
Introduces a general and more applicable theoretical formalism based on
the theory of periodic Sturm-Liouville equations for investigating
one-dimensional photonic crystals and phononic crystals
Provides a general theoretical formalism for investigating the existence
and properties of surface states/modes in semi-infinite one-dimensional
crystals