Spinor spherical

FVom the discussion above, we obtain the following two-component representations of spherical spinors for the two possible values, j = l 1/2 ... 

It follows that the spherical spinors are eigenfunctions of P having eigenvalues tt = (—1). The two spinors corresponding to the same value of j, have... 

By omitting an explicit reference to the orbital angular momentum quantum number, we may write the two sets of spherical spinors in compact form as... 

In order to elucidate whether (tr f) leaves the spherical spinor unchanged or whether it switches from the (+) to the (—) spinor of the pair (or vice versa), we study the parity properties of the spherical spinors. By operating with the parity operator P on the Pauli spinors we find... 

Schwabl provides many details on how the Dirac hydrogen atom can be solved, though some essential steps are treated very briefly. However, the material in Schw-abl s book is still more extensive than in many of the new publications on the subject. Also, the reader will find a more detailed comparison to the Klein-Gordon equation in external electromagnetic fields. But note that Schwabl chooses a different sign convention for the spherical spinors with effect on almost all equations of the Dirac hydrogen atom compared to Arose derived here. 

Das book contains a lot of material on the hydrogen atom in particular, explicit expressions for the excited state wave functions of the hydrogen atom are tabulated which we recommend for further reference. Also, alternative derivations to those presented in this volume can be found. For instance, tbe action of ([Pg.234]

Since the structure of the many-electron Dirac Hamiltonian operator for atoms allows us to separate radial and angular degrees of freedom (as in the case of the one-electron atoms solved analytically in chapter 6), the coordinates in the 4-spinor s components may be separated into radial and spherical spinor parts. 

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