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Thermodynamics
Published in Harshad K. D. H. Bhadeshia, Theory of Transformations in Steels, 2021
The spin of an electron is characterised by a spin quantum number s, which has values of ±12. The unit magnetic moment is the Bohr magneton (μB). Because the spin can be in one of two senses, the magnetic dipole of the electron either supports or opposes an applied magnetic field. A magnetic field of strength Hmag (amperes per metre) may lead to an induced magnetic dipole moment per unit volume, M. The magnetic susceptibility of the material is then given by M/Hmag. The susceptibility is negative if the induced moment opposes the applied field.
Introduction to Quantum Mechanics
Published in Caroline Desgranges, Jerome Delhommelle, A Mole of Chemistry, 2020
Caroline Desgranges, Jerome Delhommelle
Finally, Pauli (1900–1958) receives the Nobel Prize in 1945 “for the discovery of the Exclusion Principle, also called the Pauli Principle”. As we have seen, Bohr’s model of the atom postulates that electrons move in stationary orbits around the nucleus. To better characterize each of the electrons of an atom, quantum numbers are assigned and correspond to distinct energy levels and spatial extents: principal quantum number (n), the azimuthal (also known as orbital angular momentum) quantum number (l), the magnetic quantum number (m) (Figure 3.16). In 1925, Pauli introduces the spin quantum number (ms), which takes values of +1/2 or –1/2, and formulates the Pauli principle: no two electrons in an atom can have identical sets of quantum numbers. Let us add that the Pauli principle also stands for protons and neutrons.
Basic Physics of X-ray Interactions in Matter
Published in Paolo Russo, Handbook of X-ray Imaging, 2017
In contrast to the principle quantum number, n, which is (like in Bohr's model) coupled to the radial component of the wave function and describes the size of the orbit, the angular momentum quantum number, ℓ (the polar component), and the magnetic quantum number, mℓ (the azimuthal component) are required. The angular quantum number (ℓ) describes the shape of the orbital. As depicted in Figure 1.5, orbitals have shapes that are described as spherical (ℓ = 0), and with some imagination polar (ℓ = 1), or cloverleaf (ℓ = 2). They can even take on more complex shapes as the value of the angular quantum number becomes larger. There is only one way in which a sphere (ℓ = 0) can be oriented in space. For higher angular numbers and, subsequently, more complex shapes, the orbitals can point in different directions. We, therefore, need the magnetic quantum number, mℓ, to describe the orientation in space of the particular orbital. This is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.
Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration
Published in Molecular Physics, 2021
Mallikarjun Karra, Burkhard Schmidt, Bretislav Friedrich
The numerical simulations presented in this Section have been carried out as a function of the pulse duration σ for a fixed value of the pulse strength . The range of σ was varied between 0.005 and 10 in steps of 0.005, i.e. from the impulsive, non-adiabatic regime (the results for are in agreement with the theory of δ-kicks [56]) to the adiabatic limit (the results for approximate well the stationary solutions of the TDSE, Equation (3)). Owing to the rectangular pulse-shape, the present problem may be well treated in a numerically exact way by the diagonalisation of a time-independent Hamiltonian in the (numerically finite) basis of J-states (since quantum number M () is conserved). We discuss the results for other values of P thus obtained later in Section 3.2.
Predicting quadrupole relaxation enhancement peaks in proton R1-NMRD profiles in solid Bi-aryl compounds from NQR parameters
Published in Molecular Physics, 2018
Christian Gösweiner, Danuta Kruk, Evrim Umut, Elzbieta Masiewicz, Markus Bödenler, Hermann Scharfetter
Details of how to calculate the NQR powder spectrum will be the matter of the following sections, but to understand the calculation procedure, one has to know that a QN can already exhibit excitable spin transitions at zero magnetic field [26]. Depending on its nuclear spin quantum number I, one can observe – in case of half integer spins – transitions k. As is given by the product of the proton's gyromagnetic ratio times, the applied field in qualitatively the same way as the splitting of quadrupole transitions is given by times , the only determinant of the frequency locations of the transition crossings are the pure quadrupole transition frequencies of the QN at zero magnetic field (see Figure 1). These are the result of an electrical interaction between the electric field gradient (EFG) at the nucleus of interest and its quadrupole moment Q being present in the QN containing molecule.
Spin-density calculation via the graphical unitary group approach
Published in Molecular Physics, 2023
Rene F. K. Spada, Maurício P. Franco, Reed Nieman, Adelia J. A. Aquino, Ron Shepard, Felix Plasser, Hans Lischka
A wave function is an eigenfunction of the operator with quantum number , and of the operator that determines the projection on the z-axis with quantum number as Atomic units, in which , are used herein. The quantum numbers S and M assume integer values for even numbers of electrons N and half-integer values for odd N.