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The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
Spin network diagram, after Penrose In physics , a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics . From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups .
The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written m s. [ 1 ] [ 2 ] The value of m s is the component of spin angular momentum, in units of the reduced Planck constant ħ , parallel to a given direction (conventionally labelled the z –axis).
In atomic physics and quantum chemistry, Hund's rules refers to a set of rules that German physicist Friedrich Hund formulated around 1925, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. The first rule is especially important in chemistry, where it is often referred to simply as Hund's ...
The combined effect of the two operators is therefore to propagate the rotated spin to a new position, which is a hint that the correct eigenstate is a spin wave, namely a superposition of states with one reduced spin. The exchange energy penalty associated with changing the orientation of one spin is reduced by spreading the disturbance over a ...
A spin C structure is analogous to a spin structure on an oriented Riemannian manifold, [9] but uses the Spin C group, which is defined instead by the exact sequence 1 → Z 2 → Spin C ( n ) → SO ( n ) × U ( 1 ) → 1. {\displaystyle 1\to \mathbb {Z} _{2}\to \operatorname {Spin} ^{\mathbf {C} }(n)\to \operatorname {SO} (n ...
A high multiplicity state is therefore the same as a high-spin state. The lowest-energy state with maximum multiplicity usually has unpaired electrons all with parallel spin. Since the spin of each electron is 1/2, the total spin is one-half the number of unpaired electrons, and the multiplicity is the number of unpaired electrons + 1.
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics.