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For example, one can exert a kind of "torque" on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole moment—see the following section). The result is that the spin vector undergoes precession, just like a classical gyroscope. This phenomenon is known as electron spin resonance (ESR).
The atom would then be pulled toward or away from the stronger magnetic field a specific amount, depending on the value of the valence electron's spin. When the spin of the electron is + + 1 / 2 the atom moves away from the stronger field, and when the spin is − + 1 / 2 the atom moves toward it. Thus the beam of silver atoms is ...
This property is usually stated by referring to the electron as a spin-1/2 particle. [79] For such particles the spin magnitude is ħ / 2 , [84] while the result of the measurement of a projection of the spin on any axis can only be ± ħ / 2 . In addition to spin, the electron has an intrinsic magnetic moment along its spin axis ...
Here is a negative constant multiplied by the spin, so the spin magnetic moment is antiparallel to the spin. The spin–orbit potential consists of two parts. The Larmor part is connected to the interaction of the spin magnetic moment of the electron with the magnetic field of the nucleus in the co-moving frame of the electron.
In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity , [ 1 ] and was the first theory to account fully for ...
Spin and magnetic moment are in the same direction for γ > 0 (as for protons). Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency.
The general form of wavefunction for a system of particles, each with position r i and z-component of spin s z i. Sums are over the discrete variable s z , integrals over continuous positions r . For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is ...
In this, the wave function is a spinor represented by four complex-valued components: [20] two for the electron and two for the electron's antiparticle, the positron. In the non-relativistic limit, the Dirac wave function resembles the Pauli wave function for the electron. Later, other relativistic wave equations were found.