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.
Highlights
Following Ashcroft and Mermin [1], we regard the conduction electron (“electron” or “hole”) as a wave packet
The cubic cell may be chosen as the wave packet for the conduction electron
If an electron is in a continuous energy range, it will be accelerated by the electric force, following Equation (13), and the material is a conductor
Summary
Following Ashcroft and Mermin [1], we regard the conduction electron (“electron” or “hole”) as a wave packet. We shall show in the present work that if we regard the rectangular-box unit cell for the orthorhombic (ORC) crystal as the wave packet, the “electron” (“hole”) moves, following the classical equations of motion. In simple cubic (SC), tetragonal (TET) and orthorhombic (ORC) crystals, the lattices have natural orthogonal axes. Their unit cells are different only in having one (1), two (2) and three (3) different sides.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
