ABSTRACT
Abstract ................................................................................................. 256 3.1 Introduction .................................................................................. 256 3.2 Overview on The Quantum Postulates of Matter......................... 260 3.2.1 Postulate of Operators and State Functions [P1] .............. 261 3.2.2 Postulate of the Averaged Measured Values [P2] ............. 263 3.2.3 Postulate of Wave Function Basic Sets and Operators’
Commutativity [P3] .......................................................... 264 3.2.4 Postulate of the Schrödinger Equations [P4] ................... 265 3.3 Bloch’ Theorem and the Crystal Orbitals .................................... 267 3.4 Quantum Models for Crystals ...................................................... 276 3.4.1 Reciprocal Lattice ............................................................ 276 3.4.2 Quantum Models of Crystals ........................................... 286 3.4.2.1 Quantum Model of Free Electrons in Crystal ... 286 3.4.2.2 Quantum Model of Quasi-Free Electrons
in Crystals .......................................................... 293 3.4.2.3 Quantum Model of Bonding Electrons
in Crystal ........................................................... 299 3.4.3.4 Quantum Model of Tight-Binding Electrons
in Crystal ........................................................... 305 3.5 Modeling Quantum Solids ........................................................... 312 3.5.1 Fermi Distribution ............................................................ 312 3.5.2 Semiconductors and Junctions ......................................... 322
3.5.3 Moletronics ...................................................................... 335 3.6 Conclusion ................................................................................... 341 Keywords .............................................................................................. 343 References ............................................................................................. 343 Author’s Main References ........................................................... 343 Specific References ...................................................................... 344 Further Readings .......................................................................... 344
ABSTRACT
The quantum mechanics postulates are shortly revived towards of their application in providing the basic crystal Bloch theorem and of further specialization to the quantum modeling of crystals in reciprocal space, on various levels of electronic behavior from free to quasi-free, to quasi-binding, to tight-binding models, as well as for modeling solids by quantum statistical means, especially grounded on Fermi statistics driving the valence-toconducting levels’ displacements so providing the quantum framework for semiconducting electrons and to chemical related moletronics.
