Electrons with their half-integral spins are known as Fermi particles or fermions and no more than two electrons can occupy a quantum state. At absolute zero the electrons occupy energy levels from zero to a maximum value of f F, defined by [Pg.305]

This is solvable for 73 analytically for some half-integral values of n as tabulated, and numerically in general as shown on the graph. The plots show that multiple values are obtained for n = -0.5 and that a limiting value 9 = 2 is reached when n = -1. [Pg.764]

Fermions are particles that have the properties of antisymmetry and a half-integral spin quantum number, among others. [Pg.258]

V l5ini7iand S = I, respectively.. STmist be positive and can assume either integral or half-integral values, and the quantum numbers lie in the mterval [Pg.28]

Because of the approximation of all of these values to z + 1/2, it is, we suggest, justified to assume the half-integral values of the valence of hyperelectronic metals, as was done in 1949 on an empirical basis (2). [Pg.407]

Beeause Pij obeys Pij Pij = 1, the eigenvalues of the Pij operators must be +1 or -1. Eleetrons are Fermions (i.e., they have half-integral spin), and they have wavefunetions whieh are odd under permutation of any pair Pij P = - P. Bosons sueh as photons or deuterium nuelei (i.e., speeies with integral spin quantum numbers) have wavefunetions whieh obey Pij P = + P. [Pg.240]

Iron is notable for the range of electronic spin states to which it gives rise. The values of S which are found include every integral and half-integral value from 0 to i.e. every value possible for a d-block element (Table 25.4). [Pg.1079]

As a basis for subsequent discussion, we begin with a brief outline of relevant aspects of the normal n.m.r. experiment in which an assembly of nuclei with half-integral spins is observed (for a fuller treatment of the basic principles of magnetic resonance, see e.g. Carrington and MoLaohlan, 1967). [Pg.54]

Schwartz, H. M., Phys. Rev. 103, 110, "Ground state solution of the non-relativistic equation for He." More rapid convergence in the Ritz variational method by inclusion of half-integral powers in the Hylleraas function. [Pg.349]

ABSTRACT The statistical treatment of resonating covalent bonds in metals, previously applied to hypoelectronic metals, is extended to hyperelectronic metals and to metals with two kinds of bonds. The theory leads to half-integral values of the valence for hyperelectronic metallic elements. [Pg.407]

The wave fiinetion for a system of N identical particles is either symmetric or antisymmetric with respect to the interchange of any pair of the N particles. Elementary or eomposite particles with integral spins (s = 0, 1,2,. ..) possess symmetrie wave functions, while those with half-integral spins (s = 1. .) [Pg.217]

Schrodinger s equation has solutions characterized by three quantum numbers only, whereas electron spin appears naturally as a solution of Dirac s relativistic equation. As a consequence it is often stated that spin is a relativistic effect. However, the fact that half-integral angular momentum states, predicted by the ladder-operator method, are compatible with non-relativistic systems, refutes this conclusion. The non-appearance of electron [Pg.237]

There is no theoretical ground for this conclusion, which is a purely empirical result based on a variety of experimental measurements. However, it seems to apply everywhere and to represent a law of Nature, stating that systems consisting of more than one particle of half-integral spin are always represented by anti-symmetric wave functions. It is noted that if the space function is symmetrical, the spin function must be anti-symmetrical to give an anti-symmetrical product. When each of the three symmetrical states is combined with the anti-symmetrical space function this produces what is [Pg.244]

After values of a and are assumed, this equation can be integrated either analytically or numerically over the time ranges of the data. If the values of the k s are substantially constant, the correct choices of a and had been made. It is usual in this method to try only Integral or half integral values of the exponents, starting with the assumption that the rate equation conforms to the stoichiometry. [Pg.107]

Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. [Pg.30]

See also in sourсe #XX -- [ Pg.168 ]

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