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The quantum-mechanical selection rules for electric dipole radiative transitions between atomic energy levels are derived, firstly for one-electron atoms without spin, and then including spin angular momentum. The discussion is extended to many-electron atoms and rules for L, S, and J quantum numbers are derived.

This chapter discusses two ‘sacred’ principles in the current framework of physics, which are really fundamental cornerstones of the present theories: the CPT theorem and the spin-statistics connection. Experimental tests of CPT, super-selection rules, and spin and statistics are presented. Some further reading and a selection of exercises are given at the end of the chapter.

This chapter covers the rudiments of group theory, with emphasis on the use of the character tables of molecular point groups. The chapter begins with the identification of the symmetry elements a molecule possesses, and the symmetry operations these elements generate. With such knowledge at hand, the symmetry point group of a given molecule can be readily determined. The character tables of the point groups are then introduced, and the Mulliken notation for the irreducible representations is discussed in detail. Finally, the direct product of two irreducible representations is covered. The result of the direct product is used to identify the non-zero integrals in quantum chemistry and derive the selection rules in electronic spectroscopy. No rigorous mathematics is used in treating the various theories in this chapter. Instead, abstract concepts are often illustrated with examples based on real chemical compounds or practical applications.

Party leadership selection rules are a relevant type of organizational change owing to their functional importance, their visibility, and their broader applicability to the party organization as a whole. Their change may influence the competitiveness of the contest, the legitimacy and survival prospects of the leader, and the electoral performance of the party. This chapter seeks to explain changes to party leadership selection rules by analysing the frequency, timing, and characteristics of changes to leadership selection procedures over time, across parties, and across democracies. Our findings indicate that opposition status of the party, leadership change, and inclusive selectorates have a strong effect on the likelihood of selection rule reform, while the change in vote share, party age, and ideological positions are less important predictors.

Luminescence of excitons’ treats in a comprehensive way a series of luminescence manifestations of bound electron–hole pairs, i.e. excitons. First, the concept of a free Wannier exciton is introduced and a shape of the pertinent absorption spectrum is described. Then multiple luminescence effects due to the free exciton radiative recombination are discussed in direct bandgap materials (exciton–polariton luminescence and LO-phonon assisted exciton annihilation) as well as in indirect bandgap materials (no-phonon luminescence, phonon replicas). Relevant selection rules are derived. Various kinds of excitons bound to impurities (neutral and/or ionized donors and acceptors, Haynes’ rule) are dealt with. Description of the luminescence of bound multiexciton complexes follows. The application of the bound exciton concept to quantitative impurity analysis in silicon is described. Finally, the cases of excitons bound to isoelectronic impurities and of self-trapped excitons are analyzed. Whenever meaningful, a particular characteristic emission lineshape that helps to decipher experimental spectrum is pointed out.

Unlike all of the previous chapters, this one is devoted to low-dimensional semiconductor structures (quantum wells, quantum wires and quantum dots-nanocrystals). Basic classification of these structures is outlined and densities of electronic states are described. A detailed theoretical treatment of electronic states and exciton effects in quantum wells, both with infinite and finite barriers, is presented in effective-mass approximation. Strong and weak quantum confinement limits are discussed. Selection rules for optical transitions in quantum wells are outlined and optical absorption and emission spectra are compared. Specificity of exciton behaviour is stressed. Quantum dots with spherically symmetric potential are described in strong and weak quantum confinement regime. Salient luminescence features of quantum dots are summarized and illustrated via typical examples. Briefly mentioned are other interesting luminescence-related phenomena: phonon bottleneck, excitons indirect in real space, enhancement of nano-luminescence by metal nanoparticles and exciton multiplication.

Using data from the Political Party Database, this chapter analyses the impact of the internal structures and rules of political parties on women’s representation (conceptualized as the number of female candidates nominated). It examines the impact of candidate selection methods (inclusive/exclusive, centralized/decentralized), gender quotas, the presence of intra-party women’s organizations, reserved positions in party institutions, and candidacy requirements. The multivariate analysis reveals that state-level gender quotas have a significant positive effect on the number of women nominated, as does the presence of women in positions of authority, such as in parliament and on party executives. Interestingly, the authors find that the formal rules adopted by parties concerning candidate selection (including candidate selection rules) do not make a significant difference when considering representational outcomes.

This chapter brings together several themes and perspectives by exploring them in quantum-confined conditions or in monolayer crystals. In it, confinement of electrons and holes at heterostructure interfaces, in inversion layers, in quantum wells and in superlattices is analyzed using the envelope function to illustrate the variety of interactions that must be properly accounted for. The formation of subbands in confinement, minibands in superlattices, and transmission, reflection and resonance at confined barriers and wells is discussed. Propagation, screening, scattering and the behavior of shallow dopants are discussed to illustrate changes with reduction of dimensions. Particular emphasis is placed on optical transitions to illustrate the changes in selection rules for interband and intraband transitions. Confined semiconductors are contrasted with monolayer semiconductors, using graphene and nanotubes as examples whose analysis and electronic properties are discussed, to compare them with the semiconductor discussions in earlier chapters.

The development of the complex of assumptions and methods now referred to as the “old quantum theory” mainly took place in the first five years following the introduction of the Bohr atomic model in 1913. Three guiding principles emerged that were used, sometimes in overlapping ways, to explain the flood of spectroscopic data that needed to be explained. First, quantization rules (or conditions) were proposed to single out the allowed orbital motions of electrons in atoms. These rules were derived in various forms by Planck, Sommerfeld, and Wilson, but were put into their most general form by Schwarzschild, who recognized the underlying principle as the quantization of the action variables of a multiply periodic classical system. Second, the special role of the action variables in quantization was given convincing support by the transfer of the adiabatic principle of mechanics to quantum theory (work primarily due to Paul Ehrenfest). Third, the correspondence principle, or statement of asymptotic coincidence of quantum and classical theory in the limit of large quantum numbers, originally introduced by Bohr in 1913 as a supporting argument for his quantization of angular momentum in his theory of the hydrogen atom, was extended by Bohr and Kramers to provide selection rules and approximate intensity predictions evening the regime low quantum numbers.

This chapter sets out the second-quantisation treatment for systems of identical bosons or fermions. Key features such as the symmetrisation principle and super-selection rules are presented. Orthogonality and completeness requirements for mode functions are set out, and Fock states are defined in terms of mode occupancy, leading to the definitions of mode annihilation and creation operators and the determination of their commutation (bosons) or anticommutation (fermions) rules. Important two-mode states such as binomial states and relative-phase eigenstates are considered. Field creation and annihilation operators are defined and related to multi-particle position eigenstates. The Hamiltonian is expressed in terms of both mode operators and field operators, state dynamics being treated via Liouville–von Neumann, master or Matsubara equations for the density operator. Normal ordering is introduced and applied to expressions for the vacuum state projector. Multi-particle position probabilities are considered and related to normally ordered quantum correlation functions.

This chapter provides the broadest evidence on behalf of my power asymmetry argument. It begins by discussing my index of presidential powers (the dependent variable), which draws heavily from Shugart and Carey and other scholars. It then creates a measure of power asymmetry (the main independent variable): the difference between the share of seats held by Incumbent versus Opposition forces at the constituent assembly. I call this “table asymmetry.” Finally, it compares all the new constitutions to those replaced. Evidence is provided that variations in outcome are strongly correlated with variations in power asymmetry. The chapter also shows how changes in constitutions contributed to changes in regime conditions (liberal democracy declined in cases where constitutions granted presidents more power).

Professor Dicey in England and Beale in the United states propounded the ‘jurisdiction selection’ rule, according to which the law to govern a foreign contract is the law of the country where the contract is entered into, and the law to govern issues of performance is the law of the place of performance. Similarly, in the case of a foreign tort, the governing law is the law of the country where the tort is committed. This jurisdiction selection rule held sway till the first half of the twentieth century. As opposed to the above doctrine, Professor Morris propounded the ‘proper law’ rule to govern the Law of Obligations, whether it be a foreign contract or a foreign tort. According to the proper law doctrine, in Morris’s opinion, it will help achieve results which are ‘commercially convenient and sound’ in the case of foreign contracts and ‘socially convenient and sound’ in the case of foreign torts.

Niki Johnson shows that despite Uruguay being an institutionalized democracy, women have struggled to make numerical progress in politics. Formal and informal institutions that are inherently ridden with political biases limit women’s representation. Small district and party magnitudes along with male-biased candidate selection rules hindered women’s entry into office until the adoption of a gender quota, which was applied minimally by the main parties. Even with a quota, they still do not prioritize gender as a criterion for political office. Johnson points out that substantive representation of women has been historically strong. Uruguay has had a longstanding cross-party women’s caucus in the national parliament that has helped pass significant policies to help women. This contrasts with other countries where small numbers of women have meant more limited policy progress for women. Yet women still face numerous challenges both in terms of numbers and operating as women in politics in Uruguay.

Eigenstates of the square well potential are calculated and displayed. Barrier penetration and the connection to total internal reflection are explained. α‎–decay by barrier penetration is calculated and used to explain Geiger–Nuttall plots. Gauss–Hermite solutions to the harmonic oscillator potential are deduced and displayed. Zero point fluctuations are introduced. Hydrogen atom eigenstate wavefunctions for the Coulomb potential are calculated and displayed. Principal, orbital angular momentum and intrinsic angular momentum quantum numbers and their allowed combinations are discussed and interpreted: n, l, m_l, s and m_s. The Stern–Gerlach experiment and Pauli’s perception that electron spin is half-integral are presented; as are Beth’s experiment and photon spin. Dominance of electric dipole transitions and resulting selection rules discussed. Fine spectral structure and spin-orbit coupling are described. Nuclear spin and resulting hyperfine spectral structure are introduced. Landé factors introduced.

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.

This chapter addresses the free and forced oscillations of simple systems (with two or three degrees of freedom), the free oscillations of systems with the degenerate frequencies, and the eigen-oscillations of the electromechanical systems. This chapter also studies the oscillations of more complex systems using orthogonality of eigenoscillations and the symmetry properties of the system, the free oscillations of an anisotropic charged oscillator moving in a uniform constant magnetic field, and the perturbation theory adapted for the small oscillations. Finally, the chapter addresses oscillations of systems in which gyroscopic forces act and the eigen-oscillations of the simple molecules.