Electron spin magnetic moment and angular momentum

For the positive energy value we obtain two linearly independent solutions, which are 

Similarly, for the negative energy value, two new solutions are obtained, 

Electron spin magnetic moment and angular momentum 

We now show that the Dirac Hamiltonian (3.18) leads naturally to the result that the electron has an intrinsic magnetic moment arising from angular momentum of magnitude (1/2) fi, which we describe as spin angular momentum. The Dirac Hamiltonian for an electron (charge —e) in an electromagnetic field (3.18) is 

In passing from (3.30) to (3.31) we have made use of the anticommutation relations (3.14) and also of the fact that (32 = 1. It is now convenient to express a as per where ct is a three-component vector, each component of which is represented by a 4 x 4 

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Electron spin magnetic moment and angular momentum 79... 

Following the hypothesis of electron spin by Uhlenbeck and Goudsmit, P. A. M. Dirac (1928) developed a quantum mechanics based on the theory of relativity rather than on Newtonian mechanics and applied it to the electron. He found that the spin angular momentum and the spin magnetic moment of the electron are obtained automatically from the solution of his relativistic wave equation without any further postulates. Thus, spin angular momentum is an intrinsic property of an electron (and of other elementary particles as well) just as are the charge and rest mass. 

The description of the orbital and spin states of an electron in terms of the quantum numbers n, /, m, and s, and the calculation of the total angular momentum of a number of electrons in an atom in terms of J are outlined in Chapter 2. From that discussion, together with the above, it follows that an electron with orbital quantum number / possesses a total magnetic moment /(/ + and this can be oriented with respect to a magnetic field in... 

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