25 citations · 26 across the 5 of their papers we have counts for
5 papers
Quantum Confinement of Bloch Waves and Related Problems
Shang Yuan Ren
The quantum confinement of Bloch waves is fundamentally different from the well-known quantum confinement of plane waves. Unlike that obtained in the latter are all stationary stat…
Quadrupole moments, edge polarizations, and corner charges in the Wannier representation
Shang Ren, Ivo Souza, David Vanderbilt
The modern theory of polarization allows for the determination of the macroscopic end charge of a truncated one-dimensional insulator, modulo the charge quantum , from a knowled…
A special class of solutions of the truncated Hill's equation
Shang Yuan Ren
This work investigates the existence and properties of a certain class of solutions of the Hill's equation truncated in the interval [tau, tau + L] - where L = N a, a is the period…
Electronic states in ideal free standing films
Shang Yuan Ren
Exact and general results on the electronic states in ideal free standing films are presented. In many interesting cases, such as in FCC (001) films and in FCC (110) films, the ene…
Relativistic corrections to the energy spectra of completely confined particles
Shang Yuan Ren
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based…