TITLE:
Electron Dynamics in Solids
AUTHORS:
Shigeji Fujita, James McNabb III, Akira Suzuki
KEYWORDS:
Electron Dynamics, Dirac’s Theorem, Primitive Rectangular-Box Unit Cell, Wave Packet, k-Vector
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.6,
May
13,
2015
ABSTRACT: Following Ashcroft and Mermin, the
conduction electrons (“electrons” or “holes”) are assumed to move as wave
packets. Dirac’s theorem states that the quantum wave packets representing
massive particles always move, following the classical mechanical laws of
motion. It is shown here that the conduction electron in an orthorhombic
crystal moves classical mechanically if the primitive rectangular-box unit cell
is chosen as the wave packet, the condition requiring that the particle density
is constant within the cell. All crystal systems except the triclinic system
have k-vectors and energy bands. Materials are conducting if the Fermi energy
falls on the energy bands. Energy bands and gaps are calculated by using the
Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2
is a transition between conductors having three-dimensional and one-dimensional
k-vectors.