Spin component quantum number

Each electron has a spin with quantum number s = and possible <2 -components = +J, —... 

Postulate V says that an elementary particle has an internal angular momentum (spin). One can measure only two quantities the square of the spin length -I- l)h and one of its components where ms = —s, —s -I-1,..., -l-s, with spin quantum number s > 0 characteristic for the type of particle (integer for bosons, half-integer for fermions). The spin magnetic quantum number ms takes 2s -I-1 values. 

Photoelectron peaks are labelled according to the quantum numbers of the level from which the electron originates. An electron coming from an orbital with main quantum number n, orbital momentum / (0, 1, 2, 3,. .. indicated as s, p, d, f,. ..) and spin momentum s (+1/2 or -1/2) is indicated as For every orbital momentum / > 0 there are two values of the total momentum j = l+Ml and j = l-Ml, each state filled with 2j + 1 electrons. Flence, most XPS peaks come in doublets and the intensity ratio of the components is (/ + 1)//. When the doublet splitting is too small to be observed, tire subscript / + s is omitted. 

The fact that there is a one-to-one relation between the (—1) terms in the diagonal of the topological matrix and the fact that the eigenfunctions flip sign along closed contours (see discussion at the end of Section IV.A) hints at the possibility that these sign flips are related to a kind of a spin quantum number and in particular to its magnetic components. 

The general formula and the individual cases as presented in Eq. (97) indicate that indeed the number of conical intersections in a given snb-space and the number of possible sign flips within this sub-sub-Hilbert space are interrelated, similar to a spin J with respect to its magnetic components Mj. In other words, each decoupled sub-space is now characterized by a spin quantum number J that connects between the number of conical intersections in this system and the topological effects which characterize it. 

The component of the total (orbital plus electron spin) angular momentum along the intemuclear axis is Qfi, shown in Figure 7.16(a), where the quantum number Q is given by... 

The state of a particle with zero spin s = 0) may be represented by a state function (r, t) of the spatial coordinates r and the time t. However, the state of a particle having spin 5 (5 7 0) must also depend on some spin variable. We select for this spin variable the component of the spin angular momentum along the z-axis and use the quantum number ms to designate the state. Thus, for a particle in a specific spin state, the state function is denoted by (r, ms, t), where ms has only the (2s + 1) possible values —sh, (—s + )h,... 

In the presence of the applied field, B, the spin vector precesses around the direction of the field, taken by convention as the z-direction (see Figure 2.93). This precession is quantised such that the component of S in the z-direction, Sz, can only take one of two values, + 1/2 or — 1/2, and the quantum number Ms is used to label the allowed values of Sz. Thus ... 

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