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Basic Atomic and Nuclear Physics
Published in Douglas S. McGregor, J. Kenneth Shultis, Radiation Detection, 2020
Douglas S. McGregor, J. Kenneth Shultis
Each electron in an atom can be characterized by its four quantum numbers n, ℓ, m, and ms. Further, according to Pauli’s exclusion principle (1925), no two electrons in an atom can have the same quantum numbers. An assignment of a set of four quantum numbers to each electron in an atom, no sets being alike in all four numbers, then defines a quantum state for an atom as a whole. For ground-state atoms, the electrons are in the lowest energy electron states. For an atom in an excited state, one or more electrons are in electron states with energies higher than some vacant states. Electrons in excited states generally drop very rapidly (∼10−7 s) into vacant lower energy states. During these spontaneous transitions, the difference in energy levels between the two states must be emitted as a photon (fluorescence or x rays) or be absorbed by other electrons in the atom (thereby causing them to change their energy states).
STOCHASTIC ACTIVE WALKS AND POSITIVE-FEEDBACK SYSTEMS
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
In reality, interactions between any two physical entities are always indirect in nature In the microscopic level, two quantum particles interact through the exchange of a messenger. For example, two electrons repel each other by exchanging a photon. Or. in the classical language, one electron first sets up a l/r potential; the second electron "feels" this potential and experiences repulsion. Either way, the interaction is indirect. Macroscopic bodies also interact indirectly. We speak and hear each other through the sound wave in the air medium. People interact indirectly through the internet (which consists of keyboards, cables, servers, etc.) or reading an advertisement in the newspaper Instantaneous and direct interactions arc only approximations. Ultimately, all agents arc active walkers.
Crystallography, Band Structure, and Density of States at Nanoscale
Published in Sunipa Roy, Chandan Kumar Ghosh, Chandan Kumar Sarkar, Nanotechnology, 2017
Swapnadip De, Sunipa Roy, Chandan Kumar Ghosh, Chandan Kumar Sarkar
We know that the energy of the bound electron in an atom is quantized. It occupies atomic orbitals of discrete energy levels. As the atoms combine to form molecules, the atomic orbitals overlap. According to Pauli’s exclusion principle, no two electrons can have the same quantum number in a molecule. In the case of crystal lattices, a large number of identical atoms combine to form a molecule. Here the atomic orbitals split into different energy levels. A large number of closely spaced energy levels are formed. These closely spaced energy levels are known as energy bands. The finite energy gap between two energy bands is known as band gap (Figure 3.2).
Controlling observables in normal, hybrid and Josephson junctions
Published in Molecular Physics, 2018
K. J. Pototzky, A. Zacarias, E. K. U. Gross
To do similar Bell test experiments with electrons is much more difficult and remains an open challenge. In recent years, a number of ingenious experiments to create entangled electrons have been performed [79–82], going along with several theoretical developments [83–88]. The basic idea is to use a superconductor as a source of entangled electrons. In the BCS ground state, electrons form Cooper pairs due to the attractive interaction caused by phonons. These pairs consist of two electrons with opposite spin and momentum.
Two-particle coalescence conditions revisited
Published in Molecular Physics, 2022
Jacek Karwowski, Andreas Savin
We consider two Coulomb-interacting particles in a parabolic confinement, i.e. we set , and if . The radial Schrödinger Equation (1) reads where subscript ν has been replaced by the corresponding energy ϵ. In the case of two electrons (, ) the interaction is repulsive. In the case of two particles with opposite charges (electron–positron pair) – the interaction is attractive. The spectrum of the confined system () in both cases is purely discrete. In the unconfined systems () the positive energy spectrum is continuous and the continuum spreads from 0 to ∞. In the case of electron–positron pair discrete states with also appear. As it results from Equation (46), the transformation is equivalent to the replacement of by . Under this transformation the wave function changes accordingly, but the eigenvalues remain the same. Note that the last statement is valid only if the same eigenvalue exists in both repulsive and attractive cases. In particular, if then it is valid for continuous spectra. Otherwise, if , it is valid only for quasi-exact solutions of Equation (46) [17].