Search

Hereafter we shall afford the problem of the motions of the ions around their equilibrium positions in an ideal (disorder- and defect-free) crystal. The motions are called lattice vibrations. The Born-Oppenheimer separation and the adiabatic approximation (§7.1) will be implicit and the concepts involved in the description of the normal modes (§10.6) in the harmonic approximation will be used. In fact, the crystal cell will be considered as a molecular unit: its normal modes propagate along the crystal with a phase factor, in view of the spatial periodicity. [ABSTRACT FROM AUTHOR]

In the light of the main aspects involving the electronic properties, a classification of crystalline solids can be devised. This can be done either in a valence bond scenario by looking at the bonding mechanisms or by referring to the electric conduction and to the band structure. [ABSTRACT FROM AUTHOR]

A fundamental issue in solid state physics is the structure of the electronic states. Transport, magnetic and optical properties, as well as the very nature (metal, insulator or semiconductor) of the crystal, are indeed controlled by the arrangement of the energy levels. [ABSTRACT FROM AUTHOR]

In this Chapter and in the following three Chapters we shall be concerned with the general aspects of the solid state of the matter, namely the atomic arrangements where the interatomic interactions are strong enough to keep the atoms bound at well defined positions. We will address the bonding mechanisms leading to the formation of the crystals, the electronic structure and the vibrational dynamics of the atoms. The liquid and solid states are similar in many respects, for instance in regards of the density, short range structure and interactions. The difference between these two states of the matter relies on the fact that in the former the thermal energy is larger than the cohesive energy and the atoms cannot keep definite equilibrium positions. [ABSTRACT FROM AUTHOR]

In the framework of the Born-Oppenheimer separation (§ 7.1), once that the electronic state has been described and the eigenvalue Ee(R) and wavefunction φe(r,R) have been found, then the motions of the nuclei are described by a function φν(g)(R), where g represents the quantum numbers for the electrons and ν are the quantum numbers (to be found) for the nuclei. This wavefunction is solution of the Equation 10.1$$ \{ - \sum\limits_\alpha {\frac{{\hbar ^2 }} {{2M_\alpha }}\nabla _\alpha ^2 + E_e (R)\} \phi _\nu ^{(g)} } (R) = E_{g,\nu } \phi _\nu ^{(g)} (R) $$ (note that Vnn in Eq. 7.3 and 7.5 has been included in Ee(R), see for example Eq. 8.1). [ABSTRACT FROM AUTHOR]

In this Chapter a few general aspects of electronic states in polyatomic molecules shall be discussed. Some details will be given for typical molecules involving novel phenomena that do not occur in diatomic molecules. [ABSTRACT FROM AUTHOR]

In this Chapter we specialize the concepts given in Chapter 7 for the electronic states by introducing specific forms for the wavefunctions in diatomic molecules. Two main lines of description can be envisaged. In the approach known as molecular orbital (MO) the molecule is built up in a way similar to the aufbau method in atoms, namely by ideally adding electrons to one electron states. The prototype for this description is the Hydrogen molecule ion H2+. In the valence bond (VB) approach, instead, the molecule results from the interaction of atoms dressed by their electrons. The prototype in this case is the Hydrogen molecule H2. [ABSTRACT FROM AUTHOR]

In this Chapter we shall discuss the general aspects of the first state of "bonded matter", the aggregation of a few atoms to form a molecule. The related issues are also relevant for biology, medicine, astronomy etc. The knowledge of the quantum properties of the electronic states in molecules is the basis in order to create new materials, as the ones belonging to the "artificial matter", often obtained by means of subtle manipulations of atoms by means of special techniques. [ABSTRACT FROM AUTHOR]

This Chapter, dealing with nuclear and electronic angular momenta in magnetic fields, further develops topics already discussed in Chapters 4 and 5. The new arguments involve some aspects of spin statistics and of magnetic resonance (namely how to drive the angular and magnetic moments and to change their components along a magnetic field). The magnetic resonance experiment in most cases is equivalent to drive magnetic dipole transitions among Zeeman-like levels. [ABSTRACT FROM AUTHOR]

Until now the nucleus has been often considered as a point charge with infinite mass, when compared to the electron mass. The hyperfine structure in high resolution optical spectra and a variety of experiments that we shall mention at a later stage, point out that the nuclear charge is actually distributed over a finite volume. Several phenomena related to such a charge distribution occur in the atom and can be described as due to nuclear moments. [ABSTRACT FROM AUTHOR]

The analysis of the effects of magnetic or electric fields on atoms favors deeper understanding of the quantum properties of matter. Furthermore, electric or magnetic fields are tools currently used in several experimental studies. [ABSTRACT FROM AUTHOR]

By resorting to the principles of quantum mechanics and after having dealt with specific atoms, one can now proceed to the description of the electronic structure in generic multi-electron atoms. We shall see that the sequence of electron states accounts for the microscopic origin of the periodic Table of the elements. [ABSTRACT FROM AUTHOR]

Li, Na, K, Rb, Cs and Fr are a particular group of atoms characterized by one electron (often called optical being the one involved in optical spectra) with expectation value of the distance from the nucleus < r > considerably larger than the one of the remaining (N − 1) electrons, forming the internal "core". The alkali atoms are suited for analyzing the role of the core charge in modifying the Coulomb potential (−Ze2/r) pertaining to Hydrogenic atoms (§1.4), as well as to illustrate the effect of the spin-orbit interaction (§1.6). [ABSTRACT FROM AUTHOR]

The aim of this and of the following three Chapters is the derivation of the main quantum properties of the atoms and the description of their behavior in magnetic and electric fields. We shall begin in the assumption of point-charge nucleus with mass much larger than the electron mass and by taking into account only the Coulomb energy. Other interaction terms, of magnetic origin as well as the relativistic effects, will be initially disregarded. [ABSTRACT FROM AUTHOR]