Search results
Results from the WOW.Com Content Network
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 ...
If one measures the spin along a vertical axis, electrons are described as "spin up" or "spin down", based on the magnetic moment pointing up or down, respectively. To mathematically describe the experiment with spin + particles, it is easiest to use Dirac's bra–ket notation. As the particles pass through the Stern–Gerlach device, they are ...
A spinor visualized as a vector pointing along the Möbius band, exhibiting a sign inversion when the circle (the "physical system") is continuously rotated through a full turn of 360°. [a] In geometry and physics, spinors (pronounced "spinner" IPA / s p ɪ n ər /) are elements of a complex vector space that can be associated with Euclidean ...
So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector : "left" is negative, "right" is positive.
Spin can be represented by a vector whose length is measured in units of the reduced Planck constant ħ (pronounced "h bar"). For quarks, a measurement of the spin vector component along any axis can only yield the values + ħ / 2 or − ħ / 2 ; for this reason quarks are classified as spin- 1 / 2 particles. [ 70 ]
In particle physics the spin–statistics theorem implies that the wavefunction of an uncharged fermion is a section of the associated vector bundle to the spin lift of an SO(N) bundle E. Therefore, the choice of spin structure is part of the data needed to define the wavefunction, and one often needs to sum over these choices in the partition ...
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.
There are rotational matrices for each spin quantum number. Evaluating the exponential for a given z-projection spin quantum number s gives a (2s + 1)-dimensional spin matrix. This can be used to define a spinor as a column vector of 2s + 1 components which transforms to a rotated coordinate system according to the spin matrix at a fixed point ...